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Question
Solve for x:
`tan^-1 [(x-1),(x-2)] + tan^-1 [(x+1),(x+2)] = x/4`
Solution
`tan^-1 [((x-1)/(x-2)+ (x+1)/(x+2))/(1-((x-1)/(x-2)) ((x+1)/(x+2))]] = pi/4`
`((x-1)(x+2)+(x + 1)(x-2))/((x-2)(x+2)-(x-1)(x+1))= tan pi/4`
`(x^2 + 2x - x - 2+ x^2 - 2x + x-2)/((x^2-4)-(x^2-1))=1`
`(2x^2 - 4)/-3 = 1`
`2x^2 - 4 =-3 `
`2x^2 = -1`
`x^2 = 1/2`
`x = ± 1/sqrt2`
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