If or , the denominator is 0, which makes the expression undefined.

 This happens when x = 1 or when x = -2.

Therefore the correct answer is .

The two fractions on the left side of the equation need a common denominator. We can easily do find one by multiplying both the top and bottom of each fraction by the denominator of the other.

   becomes .

  becomes .

Now add the two fractions:

To solve, multiply both sides of the equation by , yielding

 .

Multiply both sides by 3:

Move all terms to the same side:

This looks like a complicated equation to factor, but luckily, the only factors of 37 are 37 and 1, so we are left with

 .

Our solutions are therefore

and

.

First, factor out x from the numerator:

Notice that the resultant expression in the parentheses is quadratic. This expression can be further factored:

We can then cancel the (x-3) which appears in both the numerator and denominator:

Finally, distribute the x outside of the parentheses to reach our answer:

Multiply each side by 

Distribute 2 to each term of the polynomial.

Divide the polynomial by 6.

Divide each side by 6.

Subtract the  term from each side.

Multiply each side by 

Distribute 3 to the terms in parentheses.

Subtract 6 from each side of the equation.

Divide each side by 3.

Multiply each side of the equation by 

Distribute 5 to each term in parentheses.

Subtract 25 from each side of equation.

Divide each side of equation by 5.

Square root of each side of equation.

First, factor the numerator. We need factors that multiply to and add to .

We can plug the factored terms into the original expression.

Note that appears in both the numerator and the denominator. This allows us to cancel the terms.

This is our final answer.

We will discuss coefficients in the general equation:

In this case,  is positive and  is negative, and , so we know our answer involves two negative numbers that are factors of  and add to . The answer is:

This is a factoring problem so we need to get all of the variables on one side and set the equation equal to zero. To do this we subtract  from both sides to get 

Think of the equation in this format to help with the following explanation.

We must then factor to find the solutions for . To do this we must make a factor tree of  which is 28 in this case to find the possible solutions. The possible numbers are , , .

Since  is positive we know that our factoring will produce two positive numbers.

We then use addition with the factoring tree to find the numbers that add together to equal . So ,  , and 

Success! 14 plus 2 equals . We then plug our numbers into the factored form of 

We know that anything multiplied by 0 is equal to 0 so we plug in the numbers for  which make each equation equal to 0 so in this case .

By factoring one gets

Now setting each of the two factors to 0 (using the zero property), one gets

or