what is x^2-25/x^2-3x-10 simplified

Question

I need to know what this is simplified. I do not think what i am getting for an answer is correct

 

Answer 1

Hi Emma-

 

Before giving you the answer please answer 2 questions:

 

How do you find the roots of a quadratic equation with the "Difference of 2 squares"?

How do you find the roots of the quadratic x^2-3x-10?

 

For the Difference of 2 squares

A^2 - B^2 the roots are (A+B)(A-B)

So for x^2-25 the roots are (x+5)(x-5)

 

For  x^2-3x-10 the roots are (x-5)(x+2)

Check using either the FOIL or "Box Method"

(x-5)(x+2) = x^2-3x-10

 

When the first set of binomials are substituted into the numerator and the second set of binomials is substituted into the denominator you get:

(x+5)(x-5)

------------

(x-5)(x+2)

 

(x-5) in the numerator and denominator cancel out to 1.

 

You simplify to get

(x+5)/(x+2)

 

Does that help?