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

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Standard XII

Mathematics

Derivative from First Principle

Solve for x...

Question

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

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Solution

$\frac{x - 1}{2 x + 1} + \frac{2 x + 1}{x - 1} = 2 (x - 1)^{2} + (2 x + 1)^{2} = 2 (x - 1) (2 x + 1) x^{2} - 2 x + 1 + 4 x^{2} + 4 x + 1 = 4 x^{2} + 2 x - 4 x - 2 x^{2} + 2 x - 4 = 0 x = \frac{- 2 \pm \sqrt{4 + 4}}{2} x = - 1 \pm \sqrt{2}$

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Solve for xx−12x+1+2x+1x−1=2 where x≠−12,1

x−12x+1+2x+1x−1=2(x−1)2+(2x+1)2=2(x−1)(2x+1)x2−2x+1+4x2+4x+1=4x2+2x−4x−2x2+2x−4=0x=−2±√4+42x=−1±√2

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

$\frac{x - 1}{2 x + 1} + \frac{2 x + 1}{x - 1} = 2 (x - 1)^{2} + (2 x + 1)^{2} = 2 (x - 1) (2 x + 1) x^{2} - 2 x + 1 + 4 x^{2} + 4 x + 1 = 4 x^{2} + 2 x - 4 x - 2 x^{2} + 2 x - 4 = 0 x = \frac{- 2 \pm \sqrt{4 + 4}}{2} x = - 1 \pm \sqrt{2}$