Question

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

Answer 1

ANSWER:

Given:

• (x +1)/(x -1) + (x -2)/(x +2) = 3; x ≠ 1, -2

To Find:

• Value of x

Solution:

We are given that,

$\implies\dfrac{x+1}{x-1}+\dfrac{x-2}{x+2}=3$

Taking LCM,

$\implies\dfrac{(x+1)(x+2)+(x-1)(x-2)}{(x-1)(x+2)}=3$

On solving brackets,

$\implies\dfrac{(x^2+x+2x+2)+(x^2-x-2x+2)}{(x^2-x+2x-2)}=3$

$\implies\dfrac{x^2+3x+2+x^2-3x+2}{(x^2+x-2)}=3$

$\implies\dfrac{2x^2+4}{(x^2+x-2)}=3$

On cross-multiplying,

$\implies2x^2+4=3(x^2+x-2)$

$\implies2x^2+4=3x^2+3x-6$

Transposing LHS to RHS,

$\implies0=3x^2+3x-6-2x^2-4$

So,

$\implies x^2+3x-10=0$

Splitting the middle term,

$\implies x^2+5x-2x-10=0$

$\implies x(x+5)-2(x+5)=0$

$\implies (x+5)(x-2)=0$

Hence,

$\implies x+5=0\:\:\&\:\:x-2=0$

Therefore,

$\implies\bf x=-5\:\:\&\:\:x=2$

Therefore, the value of x is 2 and -5.