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Solve-x-1-x-2-x-1-x-2-2x-1-x-1-2x-1-x-1-

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Question Number 217887 by ArshadS last updated on 23/Mar/25
Solve : ((x+1)/(x−2))+((x−1)/(x+2))=((2x+1)/(x−1))+((2x−1)/(x+1))
Solve:x+1x−2+x−1x+2=2x+1x−1+2x−1x+1
Answered by Rasheed.Sindhi last updated on 23/Mar/25
((x+1)/(x−2))−1+((x−1)/(x+2))−1+2=((2x+1)/(x−1))−2+((2x−1)/(x+1))−2+4 (3/(x−2))+((−3)/(x+2))=(3/(x−1))+((−3)/(x+1))+2 ((3(x+2)−3(x−2))/(x^2 −4))=((3(x+1)−3(x−1))/(x^2 −1))+2 ((3x+6−3x+6)/(x^2 −4))=((3x+3−3x+3+2x^2 −2)/(x^2 −1)) ((12)/(x^2 −4))=((4+2x^2 )/(x^2 −1)) let x^2 =y ((12)/(y−4))=((4+2y)/(y−1)) 4y−16+2y^2 −8y=12y−12 2y^2 −4y−16−12y+12=0 2y^2 −16y−4=0 y^2 −8y−2=0 y=((8±(√(64+8)))/2) =((8±6(√2))/2)=4±3(√2) x^2 =4±3(√2) x=±(√(4±3(√2)))
x+1x−2−1+x−1x+2−1+2=2x+1x−1−2+2x−1x+1−2+43x−2+−3x+2=3x−1+−3x+1+23(x+2)−3(x−2)x2−4=3(x+1)−3(x−1)x2−1+23x+6−3x+6x2−4=3x+3−3x+3+2x2−2x2−112x2−4=4+2x2x2−1letx2=y12y−4=4+2yy−14y−16+2y2−8y=12y−122y2−4y−16−12y+12=02y2−16y−4=0y2−8y−2=0y=8±64+82=8±622=4±32x2=4±32x=±4±32
Answered by Rasheed.Sindhi last updated on 23/Mar/25
Solve ((x+1)/(x−2))+((x−1)/(x+2))=((2x+1)/(x−1))+((2x−1)/(x+1)) ((x+1)/(x−2))+1+((x−1)/(x+2))+1=((2x+1)/(x−1))+1+((2x−1)/(x+1))+1 ((2x−1)/(x−2))+((2x+1)/(x+2))=((3x)/(x−1))+((3x)/(x+1)) (((2x−1)(x+2)+(2x+1)(x−2))/(x^2 −4))=((3x^2 +3x+3x^2 −3x)/(x^2 −1)) (((2x^2 −x+4x−2)+(2x^2 +x−4x−2))/(x^2 −4))=((6x^2 )/(x^2 −1)) ((4x^2 −4)/(x^2 −4))=((6x^2 )/(x^2 −1)) 4(x^2 −1)^2 =6x^2 (x^2 −4) let x^2 =y 2(y−1)^2 =3y(y−4) 2y^2 −4y+2=3y^2 −12y y^2 −8y−2=0 y=((8±(√(64+8)))/2) y=((8±6(√2))/2) x^2 =4±3(√2) x=±(√(4±3(√2)))
Solvex+1x−2+x−1x+2=2x+1x−1+2x−1x+1x+1x−2+1+x−1x+2+1=2x+1x−1+1+2x−1x+1+12x−1x−2+2x+1x+2=3xx−1+3xx+1(2x−1)(x+2)+(2x+1)(x−2)x2−4=3x2+3x+3x2−3xx2−1(2x2−x+4x−2)+(2x2+x−4x−2)x2−4=6x2x2−14x2−4x2−4=6x2x2−14(x2−1)2=6x2(x2−4)letx2=y2(y−1)2=3y(y−4)2y2−4y+2=3y2−12yy2−8y−2=0y=8±64+82y=8±622x2=4±32x=±4±32

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