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Question
Solve the following equation for x:
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
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Solution
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
`=>tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=tan^-1 1`
`=>tan^-1((x-2)/(x-1))=tan^-1 1-tan^-1((x+2)/(x+1))`
`=>tan^-1((x-2)/(x-1))=tan^-1((1-(x+2)/(x+1))/(1+(x+2)/(x+1)))`
`=>tan^-1((x-2)/(x-1))=tan^-1((x+1-x-2)/(x+1+x+2))`
`=>tan^-1((x-2)/(x-1))=tan^-1((-1)/(2x+3))`
`=>(x-2)/(x-1)=(-1)/(2x+3)`
`=>2x^2+3x-4x-6=-x+1`
`=>2x^2=1+6`
`=>x^2=7`
`=>x=+-sqrt(7/2)`
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