X 1 x 1 x 2 x 2 3

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

Answered by admin @


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

••••


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