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Question
Solve the following equation:
`1/("x" - 1) - 1/"x" = 1/("x" + 3) - 1/("x" + 4)`
Solution
`1/("x" - 1) - 1/"x" = 1/("x" + 3) - 1/("x" + 4)`
`=> ("x" - ("x" - 1))/(("x" - 1)"x") = (("x" + 4)-("x" + 3))/(("x" + 3)("x" + 4))`
`= 1/(("x" - 1)"x") = 1/(("x" + 3)("x" + 4))`
= (x + 3)(x + 4) = x(x - 1)
⇒ x2 + 4x + 3x + 12 = x2 - x
⇒ x2 + 7x - x2 + x = -12
8x = -12
x = `-12/8 = - 3/2 = - 1 1/2`
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