Solve for x. 1/x-4 + 1/x+4 = 4/x^2-16

Solve for x. 1/x-4 + 1/x+4 = 4/x^2-16
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The denominators x-4 and x+4 are the factors of x^2-16, so multiplying through by the latter gives us: x+4+x-4=4, from which 2x=4 and x=2.
by Top Rated User (1.1m points)

Given 1/(x-4) + 1/(x+4) = 4/(x^2-16)

Take LCM
[(x+4)+(x-4)]/[(x-4)(x+4)]=4/(x^2-16)
[(x+4)+(x-4)]/[x^2-16]=4/(x^2-16)
(x+4)+(x-4)=4
2x=4
x=2

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by Level 8 User (30.1k points)

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