Solve the following quadratic equation by factorization:

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

Given:

Given quadratic equation is $\frac{x-1}{2x+1}+\frac{2x+1}{x-1}=\frac{5}{2}, x ≠-\frac{1}{2},1$.

To do:

We have to solve the given quadratic equation by factorization. 

Solution:

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

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

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

$\frac{x^2-2x+1+4x^2+4x+1}{2x^2-x-1}=\frac{5}{2}$

$2(5x^2+2x+2)=5(2x^2-x-1)$   (on cross multiplication)

$10x^2+4x+4=10x^2-5x-5$

$4x+5x=-5-4$

$9x=-9$

$x=-1$

The value of $x$ is $-1$.

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Updated on: 10-Oct-2022

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