Question

`(x+3)/(x-2)-(1-x)/x=17/4` 

Answer 1

`((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`