Solve the following equation and verify your answer: x+2 x+5 = x … - Vidyadip

Question

Solve the following equation and verify your answer:
$\frac{\text{x}+2}{\text{x}+5}=\frac{\text{x}}{\text{x}+6}$

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Answer

$\frac{\text{x}+2}{\text{x}+5}=\frac{\text{x}}{\text{x}+6}$
By cross multiplication,
$(\text{x}+2)(\text{x}+6)=\text{x}(\text{x}+5)$
$\Rightarrow\text{x}^2+6\text{x}+2\text{x}+12=\text{x}^2+5\text{x}$
$\Rightarrow\text{x}^2+8\text{x}+12=\text{x}^2+5\text{x}$
$\Rightarrow\text{x}^2+8\text{x}-\text{x}^2-5\text{x}=-12$
$\Rightarrow3\text{x}$
$=-12$
$\Rightarrow\text{x}=\frac{-12}{3}$
$=-4$
$\therefore\text{x}=-4$
Verification:
$\text{L.H.S}=\frac{\text{x}+2}{\text{x}+5}=\frac{-4+2}{-4+5}=\frac{-2}{1}=-2$
$\text{R.H.S}=\frac{\text{x}}{\text{x}+6}=\frac{-4}{-4+6}=\frac{-4}{2}=-2$
$\therefore\text{L.H.S}=\text{R.H.S}$

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