Question

Solve for x
X+1/x-1+ x-2/x+2 =3

Answer 1

Hi,

( x + 1 )/( x - 1 ) + ( x - 2 )/(x + 2 ) = 3

[(x + 1 )(x + 2 ) + ( x - 2 )( x - 1 ) ]/[(x -1)(x +2 )] = 3

[ x² + 3x + 2 + x² - 3x + 2 ] / ( x² + x - 2 ) = 3

( 2x² + 4 ) = 3 ( x² + x - 2 )

2x² + 4 = 3x² + 3x - 6

0 = 3x² + 3x - 6 - 2x² - 4

x² + 3x - 10 = 0

x² + 5x - 2x - 10 = 0

x( x + 5 ) - 2(x + 5 ) = 0

( x + 5 ) ( x - 2 ) = 0

Therefore ,

x + 5 = 0 or x - 2 = 0

x = -5 or x = 2

I hope this helps you.

: )

Answer 2

Hey user here is your answer.....

----> To find- x

----> Given equation- x+1/x-1+x-2/x+2=3

----> Take LCM

◆(x+1)(x+2)+(x-2)(x-1)/(x-1)(x+2)=3

◆Open the brackets & cross multiply

◆x(x+2)+1(x+2)+x(x-1)-2(x-1)=3(x-1)(x+2)

◆x^2+2x+x+2+x^2-x-2x+2=3(x^2+2x-x-2)

◆2x^2+4=3x^2+6x-3x-6

◆2x^2+4=3x^2+3x-6

◆3x^2+3x-6-2x^2-4=0

◆x^2+3x-10=0

◆By middle term splitting

◆x^2+5x-2x-10=0

◆x(x+5)-2(x+5)=0

◆(x-2)(x+5)=0

◆x-2=0
&
x+5=0

◆x=2 & x=-5

hope it helps you☺️