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Question
Find the root of the following equation.
`1/(x+4) - 1/(x-7) = 11/30, x ≠ -4, 7`
Solution
`1/(x+4) - 1/(x-7) = 11/30`
`⇒ (x-7-x-4)/((x+4)(x-7)) = 11/30`
`⇒ (-11)/((x+4)(x-7)) = 11/30`
⇒ (x + 4)(x − 7) = −30
⇒ x2 − 3x − 28 = 30
⇒ x2 − 3x + 2 = 0
⇒ x2 − 2x − x + 2 = 0
⇒ x(x − 2) − 1(x − 2) = 0
⇒ (x − 2)(x − 1) = 0
⇒ x = 1 or 2
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