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Question
Simplify `(4x)/(x^2 - 1) - (x + 1)/(x - 1)`
Solution
`(4x)/((x + 1)(x - 1)) - (x + 1)/((x - 1))`
= `(4x - (x + 1)(x + 1))/((x + 1)(x - 1))`
= `(4x - (x^2 + 2x + 1))/((x + 1)(x - 1))`
= `(4x - x^2 - 2x - 1)/((x + 1)(x - 1))`
= `(-x^2 + 2x - 1)/((x + 1)(x - 1))`
= `(-(x^2 - 2x + 1))/((x + 1)(x - 1))`
= `(-(x - 1)(x - 1))/((x + 1)(x - 1))`
= `(1 - x)/(x + 1)`
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