Question

Find the sum. Write your answer in the simplest form. Show your work

Answer 1

Cancel out terms. X cancels out in the first term. The 4 also cancels out
0/-2x + 0/x^2-4 = x^2 -2x -4

Answer 2

Answer:

$\frac{(x+4)}{x(x+2)}$

Step-by-step explanation:

$\frac{x-4}{x^2-2x} + \frac{4}{x^2-4}$

Start by factorizing the denominators of both the terms to get:

$\frac{x-4}{x(x-2)} + \frac{4}{(x+2)(x-2)}$

Now take the LCM for both the terms to get:

$\frac{(x-4)(x-2)}{x(x-2)(x+2)} + \frac{4x}{(x-2)(x-2)x}$

Combine the fractions to get:

$\frac{(x-4)(x-2)+4x}{x(x-2)(x+2)}$

Factor 4x + (x - 4) (x + 2) to get:

$\frac{(x-2)(x+4)}{x(x-2)(x+2)}$

Cancelling the term (x - 2) to get the sum:

$\frac{(x+4)}{x(x+2)}$