x 12x+1+2x+1x 1=52 (equation is given) (x 1)^2+(2x+1)^2=52(2x+1)(x 1) x^2 2x+1+4x^2+4x+1 =52(2x^2 2x+x 1) 5x^2+2x+2=5x^2 52x 52 2x ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Linear Equation

x-12x+1+2x+1x...

Question

$\frac{x - 1}{2 x + 1} + \frac{2 x + 1}{x - 1} = \frac{5}{2}$ .

Open in App

Solution

$\frac{x - 1}{2 x + 1} + \frac{2 x + 1}{x - 1} = \frac{5}{2}$ (equation is given)
$(x - 1)^{2} + (2 x + 1)^{2} = \frac{5}{2} (2 x + 1) (x - 1)$
$x^{2} - 2 x + 1 + 4 x^{2} + 4 x + 1$
$= \frac{5}{2} (2 x^{2} - 2 x + x - 1)$
$5 x^{2} + 2 x + 2 = 5 x^{2} - \frac{5}{2} x - \frac{5}{2}$
$2 x + \frac{5}{2} x = - 2 - \frac{5}{2}$
$\frac{9}{2} x = \frac{- 9}{2}$
$x = - 1$

Suggest Corrections

Similar questions

\int \sqrt{(x^{2} + 2 x + 5)} d x

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

\int \sqrt{x^{2} + 2 x + 5} dx is equal to

4 x^{2} + 8 x + 3

(x + 1) (x + 3)

(2 x + 1) (2 x + 3)

(2 x + 2) (2 x + 5)

(2 x - 1) (2 x - 3)

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

Join BYJU'S Learning Program