Solve for x: x+1/x-1+x-2/x+2=3(x not equal to 1 , -2)
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vatsMandvi
vatsMandvi
03.01.2018
Math
Secondary School
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Solve x+1/x-1 + x-2/x+2=3
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please check the answer......
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mysticd
mysticd Genius
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:
x= -5 or 2
Step-by-step explanation:
x+1/x-1=(3x+6-x+2)/x+2
or , x+1/x-1 =2x+8/x+2
or , x²+3x+2=2x²+6x-8
or , x²+3x-10=0
or , (x+5)(x-2)=0
hence x= -5 or 2
HOPE YOU UNDERSTAND DEAR..