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# Solve for X: 1 X − 3 − 1 X + 5 = 1 6 , X ≠ 3 , − 5 - CBSE Class 10 - Mathematics

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ConceptRelationship Between Discriminant and Nature of Roots

#### Question

Solve for x: $\frac{1}{x - 3} - \frac{1}{x + 5} = \frac{1}{6}, x \neq 3, - 5$

#### Solution

$\frac{1}{x - 3} - \frac{1}{x + 5} = \frac{1}{6}$

$\Rightarrow \frac{x + 5 - x + 3}{\left( x - 3 \right)\left( x + 5 \right)} = \frac{1}{6}$

$\Rightarrow \frac{8}{\left( x - 3 \right)\left( x + 5 \right)} = \frac{1}{6}$

$\Rightarrow 48 = x^2 + 2x - 15$

$\Rightarrow x^2 + 2x - 15 - 48 = 0$

$\Rightarrow x^2 + 2x - 63 = 0$

$\Rightarrow x^2 + 9x - 7x - 63 = 0$

$\Rightarrow x\left( x + 9 \right) - 7\left( x + 9 \right) = 0$

$\Rightarrow \left( x - 7 \right)\left( x + 9 \right) = 0$

$\Rightarrow x = 7, - 9$

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#### APPEARS IN

Solution Solve for X: 1 X − 3 − 1 X + 5 = 1 6 , X ≠ 3 , − 5 Concept: Relationship Between Discriminant and Nature of Roots.
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