Question

$1 \div (x - 3) - 1 \div (x + 5) = 1 \div 6$
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Answer 1

Answer:

The value of x is -9 or 7.    

Explanation:

$\frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6}\\or,\frac{x+5-x+3}{(x-3)(x+5)}=\frac{1}{6}\\or,\frac{8}{x^{2}+5x-3x-15}=\frac{1}{6}\\or,48=x^{2}+2x-15\\or,x^{2}+2x-63=0\\or,x^{2}+9x-7x-63=0\\or,x(x+9)-7(x+9)=0\\or,(x+9)(x-7)=0$

∴$either,x+9=0$                $or,x-7=0$

⇒$x=-9$                 ⇒$x=7$

∴The value of x is -9 or 7.

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