Solve for x: 2 over x - 2 + 7 over x^2 - 4 = 5 over x

A. x = - 4/3 and x = - 5

B. x = - 4/3 and x = 5

C. x = 4/3 and x = - 5

D. x = 4/3 and x = 5

B. x = - 4/3 and x = 5

Step-by-step explanation:

2 / (x - 2) + 7 / (x² - 4) = 5 / x

2 / (x - 2) + 7 / ((x + 2) (x - 2)) = 5 / x

Multiply both sides by x - 2:

2 + 7 / (x + 2) = 5 (x - 2) / x

Multiply both sides by x + 2:

2 (x + 2) + 7 = 5 (x - 2) (x + 2) / x

Multiply both sides by x:

2x (x + 2) + 7x = 5 (x - 2) (x + 2)

Simplify:

2x² + 4x + 7x = 5 (x² - 4)

2x² + 4x + 7x = 5x² - 20

0 = 3x² - 11x - 20

Factor:

0 = (3x + 4) (x - 5)

x = - 4/3 or x = 5