Answer:
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
