How to subtract rational expressions with different denominators - ACT Math

The common denominator of these two fractions simply is the product of the two denominators, namely:

Thus, you will need to multiply each fraction's numerator and denominator by the opposite fraction's denominator:

Let's first simplify the numerator:

, which is the simplest form you will need for this question.

However, the correct answer has the denominator multiplied out. Merely FOIL :

Always start the simplification of rational expressions with quadratic denominators by factoring the denominator that has a squared element:

Thus, we need to multiply the numerator and denominator of the first term by :

Distribute:

This is simply:

You cannot factor the top in any way that would help you to cancel anything. Therefore, the answer stands as it does. You need to FOIL the denominator back out, as your correct answer is in that form:

Begin by factoring your denominators:

Therefore, the common denominator of our fractions is:

This will require you to multiply the first fraction by and the second by . This gives you:

Now, FOIL the second member and distribute the first:

Next, distribute the subtraction:

Finally, simplify:

The common denominator of these two fractions simply is the product of the two denominators, namely:

Thus, you will need to multiply each fraction's numerator and denominator by the opposite fraction's denominator:

Let's first simplify the numerator:

, which is the simplest form you will need for this question.

However, the correct answer has the denominator multiplied out. Merely FOIL :

Always start the simplification of rational expressions with quadratic denominators by factoring the denominator that has a squared element:

Thus, we need to multiply the numerator and denominator of the first term by :

Distribute:

This is simply:

You cannot factor the top in any way that would help you to cancel anything. Therefore, the answer stands as it does. You need to FOIL the denominator back out, as your correct answer is in that form:

Begin by factoring your denominators:

Therefore, the common denominator of our fractions is:

This will require you to multiply the first fraction by and the second by . This gives you:

Now, FOIL the second member and distribute the first:

Next, distribute the subtraction:

Finally, simplify:

The common denominator of these two fractions simply is the product of the two denominators, namely:

Thus, you will need to multiply each fraction's numerator and denominator by the opposite fraction's denominator:

Let's first simplify the numerator:

, which is the simplest form you will need for this question.

However, the correct answer has the denominator multiplied out. Merely FOIL :

Always start the simplification of rational expressions with quadratic denominators by factoring the denominator that has a squared element:

Thus, we need to multiply the numerator and denominator of the first term by :

Distribute:

This is simply:

You cannot factor the top in any way that would help you to cancel anything. Therefore, the answer stands as it does. You need to FOIL the denominator back out, as your correct answer is in that form:

Begin by factoring your denominators:

Therefore, the common denominator of our fractions is:

This will require you to multiply the first fraction by and the second by . This gives you:

Now, FOIL the second member and distribute the first:

Next, distribute the subtraction:

Finally, simplify:

The common denominator of these two fractions simply is the product of the two denominators, namely:

Thus, you will need to multiply each fraction's numerator and denominator by the opposite fraction's denominator:

Let's first simplify the numerator:

, which is the simplest form you will need for this question.

However, the correct answer has the denominator multiplied out. Merely FOIL :

Always start the simplification of rational expressions with quadratic denominators by factoring the denominator that has a squared element:

Thus, we need to multiply the numerator and denominator of the first term by :

Distribute:

This is simply:

You cannot factor the top in any way that would help you to cancel anything. Therefore, the answer stands as it does. You need to FOIL the denominator back out, as your correct answer is in that form:

Begin by factoring your denominators:

Therefore, the common denominator of our fractions is:

This will require you to multiply the first fraction by and the second by . This gives you:

Now, FOIL the second member and distribute the first:

Next, distribute the subtraction:

Finally, simplify:

The common denominator of these two fractions simply is the product of the two denominators, namely:

Thus, you will need to multiply each fraction's numerator and denominator by the opposite fraction's denominator:

Let's first simplify the numerator:

, which is the simplest form you will need for this question.

However, the correct answer has the denominator multiplied out. Merely FOIL :

Always start the simplification of rational expressions with quadratic denominators by factoring the denominator that has a squared element:

Thus, we need to multiply the numerator and denominator of the first term by :

Distribute:

This is simply:

You cannot factor the top in any way that would help you to cancel anything. Therefore, the answer stands as it does. You need to FOIL the denominator back out, as your correct answer is in that form:

Begin by factoring your denominators:

Therefore, the common denominator of our fractions is:

This will require you to multiply the first fraction by and the second by . This gives you:

Now, FOIL the second member and distribute the first:

Next, distribute the subtraction:

Finally, simplify:

The common denominator of these two fractions simply is the product of the two denominators, namely:

Thus, you will need to multiply each fraction's numerator and denominator by the opposite fraction's denominator:

Let's first simplify the numerator:

, which is the simplest form you will need for this question.

However, the correct answer has the denominator multiplied out. Merely FOIL :

Always start the simplification of rational expressions with quadratic denominators by factoring the denominator that has a squared element:

Thus, we need to multiply the numerator and denominator of the first term by :

Distribute:

This is simply:

You cannot factor the top in any way that would help you to cancel anything. Therefore, the answer stands as it does. You need to FOIL the denominator back out, as your correct answer is in that form:

Begin by factoring your denominators:

Therefore, the common denominator of our fractions is:

This will require you to multiply the first fraction by and the second by . This gives you:

Now, FOIL the second member and distribute the first:

Next, distribute the subtraction:

Finally, simplify:

The common denominator of these two fractions simply is the product of the two denominators, namely:

Thus, you will need to multiply each fraction's numerator and denominator by the opposite fraction's denominator:

Let's first simplify the numerator:

, which is the simplest form you will need for this question.

However, the correct answer has the denominator multiplied out. Merely FOIL :

Always start the simplification of rational expressions with quadratic denominators by factoring the denominator that has a squared element:

Thus, we need to multiply the numerator and denominator of the first term by :

Distribute:

This is simply:

You cannot factor the top in any way that would help you to cancel anything. Therefore, the answer stands as it does. You need to FOIL the denominator back out, as your correct answer is in that form: