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Solve for x : (x+1)/(x-1)+(x-1)/(x+2)=4-(2x+3)/(x-2); x!=1, -2, 2 - Mathematics

Solve for x : `(x+1)/(x-1)+(x-1)/(x+2)=4-(2x+3)/(x-2);x!=1,-2,2`

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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)(x2)=(2x11)(x2+x2)

2x34x2+4x8=2x3+2x24x11x211x+22

2x34x2+4x8=2x39x215x+22

2x32x34x2+9x2+4x+15x822=0

5x2+19x30=0

5x2+25x6x30=0

5x(x+5)6(x+5)=0

(5x6)(x+5)=0

5x6=0, x+5=0

x=`6/5`, x=5

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