# How do you solve #(x+2)/(x+3)-1=1/(3-2x-x^2)# and check for extraneous solutions?

##### 1 Answer

May 13, 2017

#### Answer:

Please see the explanation.

#### Explanation:

Given:

Multiply the right side by 1 in the form of

Factor the right side's denominator:

Restrict the domain to prevent division by 0:

NOTE: We restrict the values of x to make us notice, if we obtain an extraneous root.

Multiply both sides by

Combine like terms:

Multiply both sides by

Add 1 to both sides and drop the restrictions, because the solution will not violate them.

Check:

This checks.