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

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