Question

Q.Find the value of x and verify it :-
=> $\sf\large\red{ \frac{1}{x \: + \: 3} \: - \: \frac{x}{x^2 \: - \: 9} \: = \: \frac{2}{3 \: - \: x}}$
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Answer 1

Given Equation:

$\longrightarrow\sf \: \frac{1}{x + 3} - \frac{x}{ {x}^{2} - 9} = \frac{2}{3 - x}$

$\sf $

$\longrightarrow\sf \frac{x-3-x}{x^2-9}=\frac{2}{3-x}$

$\longrightarrow\sf \frac{3}{9-x^2}=\frac{2}{3-x}$

$\longrightarrow\sf \frac{3}{(3-x)(3+x)}=\frac{2}{3-x}$

$\longrightarrow\sf \frac{3}{3+x}=2$

$\longrightarrow\sf 3=6+2x$

$\longrightarrow\sf 2x=-3$

$\longrightarrow\sf x=-\frac{3}{2}$

$\longrightarrow\sf x=-1.5$

So, The value of x satisfying the given equation is -1.5