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Solve forx :- (X/x-1)-x-1/x=34/15,x not equal 0,x not equal -1

Posted by Romal Shahare 5 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 5 years, 10 months ago

Given,
$\frac { x } { x + 1 } + \frac { x + 1 } { x } = \frac { 34 } { 15 }$

Taking LCM, we get
$\Rightarrow \quad \frac { x ^ { 2 } + ( x + 1 ) ^ { 2 } } { x ( x + 1 ) } = \frac { 34 } { 15 }$
$\Rightarrow \quad \frac { x ^ { 2 } + x ^ { 2 } + 2 x + 1 } { x ^ { 2 } + x } = \frac { 34 } { 15 }$
After cross multiplication,we get
$\Rightarrow$ 34x² + 34x = 15x²+ 15x²+ 30x +15
$\Rightarrow$ 4x² + 4x - 15 = 0
$\Rightarrow$ 4x² + 10x - 6x - 15 = 0
$\Rightarrow$ (2x - 3)(2x + 5) = 0 $\Rightarrow$ 2x - 3 = 0 or, 2x + 5 = 0 $\Rightarrow$ $x = \frac { 3 } { 2 } \text { or } x = - \frac { 5 } { 2 }$

0Thank You

ANSWER

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CBSE > Class 10 > Mathematics