Solve - x-12x-1 - 2x-1x-1 -2 - where x - -12- 1

x 12x+1 + 2x+1x 1 =2 #160; (x 1)^2 + (2x+1)^2(2x+1)(x 1)=2 x^2+1 2x+4x^2+1+4x =(2x 2)(2x+1) 5x^2+2x+2 = 4x^2+2x 4x 2 x^2+4x+4=0 ...

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Byju's Answer

Standard XII

Mathematics

Integration by Parts

Solve : x-1...

Question

Solve : $\frac{x - 1}{2 x + 1} + \frac{2 x + 1}{x - 1} = 2$ , where $x \neq - \frac{1}{2}, 1$

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Solution

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

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

$x^{2} + 1 - 2 x + 4 x^{2} + 1 + 4 x = (2 x - 2) (2 x + 1)$
$5 x^{2} + 2 x + 2 = 4 x^{2} + 2 x - 4 x - 2$
$x^{2} + 4 x + 4 = 0$
$x^{2} + 2 x + 2 x + 4 = 0$
$x (x + 2) + 2 (x + 2) = 0$
$(x + 2) (x + 2) = 0$
$x = - 2, - 2$

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Similar questions

Q. Solve for

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

where

x \neq \frac{- 1}{2}, 1

Solve each of the following quadratic equations:
(i) $\frac{x}{x - 1} + \frac{x - 1}{x} = 4 \frac{1}{4}, x \neq 0, 1$
(ii) $\frac{x - 1}{2 x - 1} + \frac{2 x - 1}{x - 1} = 2, x \neq \frac{1}{2}, 1$

Q. Solve the following quadratic equation by factorization, the root is :

- 1

and

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\frac{x - 1}{2 x + 1} + \frac{2 x + 1}{x - 1} = \frac{5}{2}, x \neq - \frac{1}{2}, 1

\frac{x - 1}{2 x + 1} + \frac{2 x + 1}{x - 1} = \frac{5}{2}, x \neq - \frac{1}{2}, 1

Q. Solve the following equation:

\sqrt{\frac{2 x + 1}{x - 1}} - 2 \sqrt{\frac{x - 1}{2 x + 1}} = 1

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Solve : x−12x+1+2x+1x−1=2 , where x≠−12,1

x−12x+1+2x+1x−1=2 (x−1)2+(2x+1)2(2x+1)(x−1)=2x2+1−2x+4x2+1+4x=(2x−2)(2x+1)5x2+2x+2=4x2+2x−4x−2x2+4x+4=0x2+2x+2x+4=0x(x+2)+2(x+2)=0(x+2)(x+2)=0x=−2,−2

Solve : $\frac{x - 1}{2 x + 1} + \frac{2 x + 1}{x - 1} = 2$ , where $x \neq - \frac{1}{2}, 1$