Question

find the roots of the following equation 1/x+3 - 1/x-6 = 9/20

Answer 1

the roots are x = 2 and x = 1
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Answer 2

Answer:

x=2 or x = 1

Explanation:

$\frac{1}{x+3}+\frac{1}{x-6}=\frac{9}{20}$

$\implies \frac{x-6-(x+3)}{(x+3)(x-6)}=\frac{9}{20}$

$\implies \frac{x-6-x-3}{x^{2}-6x+3x-18}=\frac{9}{20}$

$\implies \frac{-9}{x^{2}-3x-18}=\frac{9}{20}$

$\implies 20=\frac{9(x^{2}-3x-18)}{-9}$

$\implies 20=-(x^{2}-3x-18)$

$\implies x^{2}-3x-18+20=0$

$\implies x^{2}-3x+2=0$

splitting the middle term, we get

$\implies x^{2}-2x-1x+2=0$

$\implies x(x-2)-1(x-2)=0$

$\implies (x-2)(x-1)=0$

$\implies x-2=0 \: Or \: x-1 = 0$

$\implies x = 2 \: or \: x = 1$

Therefore,.

x = 2 Or x =1

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