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Question
`(x+3)/(x-2)-(1-x)/x=17/4`
Solution
`((x+3))/((x-2))-((1-x))/x=17/4`
⇒`( x(x+3)-(1-x)(x-2))/((x-2)x)=17/4`
⇒` x^2+3x-(x-2-x^2+2x)/(x^2-2x)=17/4`
⇒ `(x^2+3x+x^2-3x+2)/(x^2-2x)=17/4`
⇒ `(2x^2+2)/(x^2-2x)=17/4`
⇒`8x^2+8=17x^2-34x` [On cross multiplying]
⇒` -9x^2+34x-8=0`
⇒` 9x^2-34x-8=0`
⇒`9x(x-4) +2(x-4)=0`
⇒`(x-4) (9x+2)=0`
⇒`x-4=0 or 9x+2=0`
⇒` x=4 or x=(-2)/9`
Hence, the roots of the equation are 4 and `-2/9`
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