How to add rational expressions with different denominators - ACT Math
Card 0 of 45
Simplify the following expression:
Simplify the following expression:
In order to add fractions, we must first make sure they have the same denominator.
So, we multiply 
by 
and get the following:
Then, we add across the numerators and simplify:
In order to add fractions, we must first make sure they have the same denominator.
So, we multiply
Then, we add across the numerators and simplify:
Compare your answer with the correct one above
Simplify the following:
Simplify the following:
To simplify the following, a common denominator must be achieved. In this case, the first term must be multiplied by (x+2) in both the numerator and denominator and likewise with the second term with (x-3).
To simplify the following, a common denominator must be achieved. In this case, the first term must be multiplied by (x+2) in both the numerator and denominator and likewise with the second term with (x-3).
Compare your answer with the correct one above
Simplify the following 
Simplify the following
Find the least common denominator between x-3 and x-4, which is (x-3)(x-4). Therefore, you have 
. Multiplying the terms out equals 
. Combining like terms results in 
.
Find the least common denominator between x-3 and x-4, which is (x-3)(x-4). Therefore, you have
Compare your answer with the correct one above
Select the expression that is equivalent to
Select the expression that is equivalent to
To add the two fractions, a common denominator must be found. With one-term denominators, it is easier to simply find the least common denominator between them and multiply each side to obtain it.
In this case, the least common denominator between 
and 
is 
. So the first fraction needs to be multiplied by 
and the second by 
:
Now, we can add straight across, remembering to combine terms where we can.
So, our simplified answer is 
To add the two fractions, a common denominator must be found. With one-term denominators, it is easier to simply find the least common denominator between them and multiply each side to obtain it.
In this case, the least common denominator between
Now, we can add straight across, remembering to combine terms where we can.
So, our simplified answer is
Compare your answer with the correct one above
Combine the following two expressions if possible.
Combine the following two expressions if possible.
For binomial expressions, it is often faster to simply FOIL them together to find a common trinomial than it is to look for individual least common denominators. Let's do that here:
FOIL and simplify.
Combine numerators.
Thus, our answer is 
For binomial expressions, it is often faster to simply FOIL them together to find a common trinomial than it is to look for individual least common denominators. Let's do that here:
FOIL and simplify.
Combine numerators.
Thus, our answer is
Compare your answer with the correct one above
Simplify the following expression:
Simplify the following expression:
In order to add fractions, we must first make sure they have the same denominator.
So, we multiply by and get the following:
Then, we add across the numerators and simplify:
In order to add fractions, we must first make sure they have the same denominator.
So, we multiply
Then, we add across the numerators and simplify:
Compare your answer with the correct one above
Simplify the following:
Simplify the following:
To simplify the following, a common denominator must be achieved. In this case, the first term must be multiplied by (x+2) in both the numerator and denominator and likewise with the second term with (x-3).
To simplify the following, a common denominator must be achieved. In this case, the first term must be multiplied by (x+2) in both the numerator and denominator and likewise with the second term with (x-3).
Compare your answer with the correct one above
Simplify the following
Simplify the following
Find the least common denominator between x-3 and x-4, which is (x-3)(x-4). Therefore, you have . Multiplying the terms out equals . Combining like terms results in .
Find the least common denominator between x-3 and x-4, which is (x-3)(x-4). Therefore, you have
Compare your answer with the correct one above
Select the expression that is equivalent to
Select the expression that is equivalent to
To add the two fractions, a common denominator must be found. With one-term denominators, it is easier to simply find the least common denominator between them and multiply each side to obtain it.
In this case, the least common denominator between and is . So the first fraction needs to be multiplied by and the second by :
Now, we can add straight across, remembering to combine terms where we can.
So, our simplified answer is
To add the two fractions, a common denominator must be found. With one-term denominators, it is easier to simply find the least common denominator between them and multiply each side to obtain it.
In this case, the least common denominator between
Now, we can add straight across, remembering to combine terms where we can.
So, our simplified answer is
Compare your answer with the correct one above
Combine the following two expressions if possible.
Combine the following two expressions if possible.
For binomial expressions, it is often faster to simply FOIL them together to find a common trinomial than it is to look for individual least common denominators. Let's do that here:
FOIL and simplify.
Combine numerators.
Thus, our answer is
For binomial expressions, it is often faster to simply FOIL them together to find a common trinomial than it is to look for individual least common denominators. Let's do that here:
FOIL and simplify.
Combine numerators.
Thus, our answer is
Compare your answer with the correct one above
Simplify the following expression:
Simplify the following expression:
In order to add fractions, we must first make sure they have the same denominator.
So, we multiply by and get the following:
Then, we add across the numerators and simplify:
In order to add fractions, we must first make sure they have the same denominator.
So, we multiply
Then, we add across the numerators and simplify:
Compare your answer with the correct one above
Simplify the following:
Simplify the following:
To simplify the following, a common denominator must be achieved. In this case, the first term must be multiplied by (x+2) in both the numerator and denominator and likewise with the second term with (x-3).
To simplify the following, a common denominator must be achieved. In this case, the first term must be multiplied by (x+2) in both the numerator and denominator and likewise with the second term with (x-3).
Compare your answer with the correct one above
Simplify the following
Simplify the following
Find the least common denominator between x-3 and x-4, which is (x-3)(x-4). Therefore, you have . Multiplying the terms out equals . Combining like terms results in .
Find the least common denominator between x-3 and x-4, which is (x-3)(x-4). Therefore, you have
Compare your answer with the correct one above
Select the expression that is equivalent to
Select the expression that is equivalent to
To add the two fractions, a common denominator must be found. With one-term denominators, it is easier to simply find the least common denominator between them and multiply each side to obtain it.
In this case, the least common denominator between and is . So the first fraction needs to be multiplied by and the second by :
Now, we can add straight across, remembering to combine terms where we can.
So, our simplified answer is
To add the two fractions, a common denominator must be found. With one-term denominators, it is easier to simply find the least common denominator between them and multiply each side to obtain it.
In this case, the least common denominator between
Now, we can add straight across, remembering to combine terms where we can.
So, our simplified answer is
Compare your answer with the correct one above
Combine the following two expressions if possible.
Combine the following two expressions if possible.
For binomial expressions, it is often faster to simply FOIL them together to find a common trinomial than it is to look for individual least common denominators. Let's do that here:
FOIL and simplify.
Combine numerators.
Thus, our answer is
For binomial expressions, it is often faster to simply FOIL them together to find a common trinomial than it is to look for individual least common denominators. Let's do that here:
FOIL and simplify.
Combine numerators.
Thus, our answer is
Compare your answer with the correct one above
Simplify the following expression:
Simplify the following expression:
In order to add fractions, we must first make sure they have the same denominator.
So, we multiply by and get the following:
Then, we add across the numerators and simplify:
In order to add fractions, we must first make sure they have the same denominator.
So, we multiply
Then, we add across the numerators and simplify:
Compare your answer with the correct one above
Simplify the following:
Simplify the following:
To simplify the following, a common denominator must be achieved. In this case, the first term must be multiplied by (x+2) in both the numerator and denominator and likewise with the second term with (x-3).
To simplify the following, a common denominator must be achieved. In this case, the first term must be multiplied by (x+2) in both the numerator and denominator and likewise with the second term with (x-3).
Compare your answer with the correct one above
Simplify the following
Simplify the following
Find the least common denominator between x-3 and x-4, which is (x-3)(x-4). Therefore, you have . Multiplying the terms out equals . Combining like terms results in .
Find the least common denominator between x-3 and x-4, which is (x-3)(x-4). Therefore, you have
Compare your answer with the correct one above
Select the expression that is equivalent to
Select the expression that is equivalent to
To add the two fractions, a common denominator must be found. With one-term denominators, it is easier to simply find the least common denominator between them and multiply each side to obtain it.
In this case, the least common denominator between and is . So the first fraction needs to be multiplied by and the second by :
Now, we can add straight across, remembering to combine terms where we can.
So, our simplified answer is
To add the two fractions, a common denominator must be found. With one-term denominators, it is easier to simply find the least common denominator between them and multiply each side to obtain it.
In this case, the least common denominator between
Now, we can add straight across, remembering to combine terms where we can.
So, our simplified answer is
Compare your answer with the correct one above
Combine the following two expressions if possible.
Combine the following two expressions if possible.
For binomial expressions, it is often faster to simply FOIL them together to find a common trinomial than it is to look for individual least common denominators. Let's do that here:
FOIL and simplify.
Combine numerators.
Thus, our answer is
For binomial expressions, it is often faster to simply FOIL them together to find a common trinomial than it is to look for individual least common denominators. Let's do that here:
FOIL and simplify.
Combine numerators.
Thus, our answer is
Compare your answer with the correct one above