Find the roots of the following equations: \frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}, x ≠ -4, 7

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Solution:

⇒ Given

$Find the roots of the following equations: \frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}, x ≠ -4, 7,Chapter-4,Exercise-4.3,Math- Class 10,$

$\large \Rightarrow -30=\left ( x+4 \right )\left ( x-7 \right )$
$\large \Rightarrow -30=x^2-7x+4x-28$
$\large \Rightarrow x^2-3x-28+30=0$
$\large \Rightarrow x^2-3x+2=0$
⇒ Finding roots by middle term factorization
$Find the roots of the following equations: \frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}, x ≠ -4, 7,Chapter-4,Exercise-4.3,Math- Class 10,⇒ Finding roots by middle term factorization$
$\large \Rightarrow x^2-2x-x+2=0$
$\large \Rightarrow x\left ( x-2 \right )-1\left ( x-2 \right )=0$
$\large \Rightarrow \left ( x-2 \right )\left ( x-1 \right )=0$
$\large \Rightarrow x-2=0,\Rightarrow x-1=0$
$\large \Rightarrow x=2,\Rightarrow x=1$
$\large \Rightarrow x=2,1$

Find the roots of the following equations: \frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}, x ≠ -4, 7

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