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:

First, pull out a common factor of 2 to get 2(2x2 + 5x – 3). Then factor the quadratic so that the x terms add to 5x and the numbers multiply to - 3, resulting in 2(2x – 1)(x + 3).

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:

The easy way to solve this problem is to multiply both halves of the fraction by the conjugate of the denominator, since this will eliminate the radical in the denominator.

Conjugate the fraction.

Next, simplify the fraction, eliminating any terms you can along the way.

Thus, is our answer.

First, pull out a common factor of 2 to get 2(2x2 + 5x – 3). Then factor the quadratic so that the x terms add to 5x and the numbers multiply to - 3, resulting in 2(2x – 1)(x + 3).

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:

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:

First, pull out a common factor of 2 to get 2(2x2 + 5x – 3). Then factor the quadratic so that the x terms add to 5x and the numbers multiply to - 3, resulting in 2(2x – 1)(x + 3).

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 by and get the following:

Then, we add across the numerators and simplify: