Factor by grouping.

For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .

Factor out of .

Rewrite as plus

Apply the distributive property.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

Factor out the greatest common factor (GCF) from each group.

Factor the polynomial by factoring out the greatest common factor, .

Factor using the perfect square rule.

Rewrite as .

Check the middle term by multiplying and compare this result with the middle term in the original expression.

Simplify.

Factor using the perfect square trinomial rule , where and .

To write as a fraction with a common denominator, multiply by .

To write as a fraction with a common denominator, multiply by .

Multiply and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Multiply and .

Reorder the factors of .

Combine the numerators over the common denominator.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Apply the distributive property.

Multiply by .

Apply the distributive property.

Multiply by .

Multiply by .

Subtract from .

Add and .

Subtract (5x)/(2x^2+5x-3)-(2x)/(x^2+6x+9)