Question

Simplify the expression: [(x^2-4)/(x-8)]/[(x-2)/(x-3)].

a) (x-4)/(x-2)
b) (x+2)/(x-3)
c) (x-3)/(x+2)
d) (x-4)/(x+2)

Answer 1

To simplify the expression [(x^2-4)/(x-8)]/[(x-2)/(x-3)], multiply the numerators and denominators, factor the numerator and denominator, and cancel out the common factors (x-2). The simplified expression is (x+2)/(x-8).

Step-by-step explanation:

To simplify the expression [(x^2-4)/(x-8)]/[(x-2)/(x-3)], we can start by multiplying the numerators and denominators of the fraction in the numerator and the fraction in the denominator. This results in [(x^2-4)(x-3)]/[(x-8)(x-2)].

Next, we can factor the numerator and denominator. The numerator can be factored as (x+2)(x-2) and the denominator can be factored as (x-8)(x-2).

Cancel out the common factors of (x-2) in the numerator and denominator. The simplified expression is (x+2)/(x-8).