Question

solve x+1/x-1 + x-2/x+2=3

Answer 1

Answer:

x= -5 or 2

Explanation:

It is given that,

$\frac{x+1}{x-1}+\frac{x-2}{x+2}=3$

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

$\implies\frac{x^{2}+2x+x+2+x^{2}-x-2x+2}{x^{2}+2x-x-2}=3$

$\implies\frac{2x^{2}+4}{x^{2}+x-2}=3$

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

$\implies 2x^{2}+4=3x^{2}+3x-6$

$\implies 0=3x^{2}+3x-6-2x^{2}-4$

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

/* Splitting the middle term,we get */

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

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

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

=> x+5 = 0 Or x-2 = 0

=> x = -5 or x = 2

Therefore,

x = -5 Or 2

••••

Answer 2

Answer:

5,-2

Step-by-step explanation:

t is given that,

/* Splitting the middle term,we get */

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

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

=> x+5 = 0 Or x-2 = 0

=> x = -5 or x = 2

Therefore,

x = -5 Or 2