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Question
Solve the following quadratic equations by factorization:
`1/(x+4)-1/(x-7)=11/30` , x ≠ 4, 7
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Solution
We have been given
`1/(x+4)-1/(x-7)=11/30`
`(-11)/(x^2-3x-28)=11/30`
-30 = x2 - 3x - 28
x2 - 3x - 28 + 30 = 0
x2 - 3x + 2 = 0
x2 - 2x - x + 2 = 0
x(x - 2) - 1(x - 2) = 0
(x - 1)(x - 2) = 0
Therefore,
x - 1 = 0
x = 1
or,
x - 2 = 0
x = 2
Hence, x = 1 or x = 2.
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