Question

Find the sum. Write your answer in simplest form: (x-4)/(x^2-2x) + 4/(x^2-4)

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

Answer 1

To find the sum, we need to find a common denominator for the two fractions and combine the numerators. The simplified sum is x^3 + 2x^2 - 12x + 16.

Step-by-step explanation:

To find the sum, we need to find a common denominator for the two fractions. The common denominator is (x^2-2x)(x^2-4). We then convert the fractions to have this common denominator:

(x-4)/(x^2-2x) * (x^2-4)/(x^2-4) + 4/(x^2-4) * (x^2-2x)/(x^2-2x)

Next, we combine the numerators:

(x^2-4)(x-4) + 4(x^2-2x)

Expanding and collecting like terms:

x^3 - 2x^2 - 4x + 16 + 4x^2 - 8x

Simplifying:

x^3 + 2x^2 - 12x + 16

The simplified sum is x^3 + 2x^2 - 12x + 16.