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Question
Solve the following quadratic equations by factorization:
`1/(x-1)-1/(x+5)=6/7` , x ≠ 1, -5
Solution
We have been given
`1/(x-1)-1/(x+5)=6/7`
`6/(x^2+4x-5)=6/7`
x2 + 4x - 12 = 0
x2 + 6x - 2x - 12 = 0
x(x + 6) - 2(x + 6) = 0
(x + 6)(x - 2) = 0
Therefore,
x - 2 = 0
x = 2
or,
x + 6 = 0
x = -6
Hence, x = 2 or x = -6
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