Question

How do you factor `(x^2-81)/( 2x^2-23x+45)`?

Answer 1

`(x+9)/(2x-5)`

Explanation:

Numerator is a Difference of Squares:
`x^2 - 81 = (x-9)(x+9)`

Denominator can be factored. I like using Mustang Method.
(Youtube: Mustang Method)
`2x^2 - 23x + 45 = (2x - 5)(x - 9)`

`(x^2-81)/(2x^2 - 23x + 45) = ((x-9)(x+9))/((2x-5)(x-9))`
Cancel Like Factors from Numerator and Denominator
`= (x+9)/(2x-5)`