Solve the following quadratic equation by factorization:

$\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{5}{6}, x ≠1,-1$

Given:

Given quadratic equation is $\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{5}{6}, x ≠1,-1$.

To do:

We have to solve the given quadratic equation by factorization. 

Solution:

$\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{5}{6}$

$\frac{(x+1)(x+1)-(x-1)(x-1)}{(x-1)(x+1)}=\frac{5}{6}$

$\frac{x^2+x+x+1-(x^2-x-x+1)}{x^2-1^2}=\frac{5}{6}$

$\frac{x^2+2x+1-x^2+2x-1}{x^2-1}=\frac{5}{6}$

$6(4x)=5(x^2-1)$   (on cross multiplication)

$24x=5x^2-5$

$5x^2-24x-5=0$

$5x^2-25x+x-5=0$

$5x(x-5)+1(x-5)=0$

$(5x+1)(x-5)=0$

$5x+1=0$ or $x-5=0$

$5x=-1$ or $x=5$

$x=-\frac{1}{5}$ or $x=5$

The roots of the given quadratic equation are $-\frac{1}{5}$ and $5$.  

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Updated on: 10-Oct-2022

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