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Question
Solve for x : `(x+1)/(x-1)+(x-1)/(x+2)=4-(2x+3)/(x-2);x!=1,-2,2`
Solution
`(x+1)/(x-1)+(x-2)/(x+2)=4-(2x+3)/(x-2)`
`=>((x+1)(x+2)+(x-1)(x-2))/((x-1)(x+2))=(4(x-2)-(2x+3))/(x-2)`
`=>((x^2+2x+x+2)+(x^2-2x-x+2))/(x^2+2x-x-2)=(4x-8-2x-3)/(x-2)`
`=>(x^2+3x+2+x^2-3x+2)/(x^2+x-2)=(2x-11)/(x-2)`
`=>(2x^2+4)/(x^2+x-2)=(2x-11)/(x-2)`
⇒(2x2+4)(x−2)=(2x−11)(x2+x−2)
⇒2x3−4x2+4x−8=2x3+2x2−4x−11x2−11x+22
⇒2x3−4x2+4x−8=2x3−9x2−15x+22
⇒2x3−2x3−4x2+9x2+4x+15x−8−22=0
⇒5x2+19x−30=0
⇒5x2+25x−6x−30=0
⇒5x(x+5)−6(x+5)=0
⇒(5x−6)(x+5)=0
⇒5x−6=0, x+5=0
⇒x=`6/5`, x=−5
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