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# Solve the Following Quadratic Equations by Factorization: - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### Question

Solve the following quadratic equations by factorization: $\frac{16}{x} - 1 = \frac{15}{x + 1}; x \neq 0, - 1$

#### Solution

$\frac{16}{x} - 1 = \frac{15}{x + 1}$

$\Rightarrow \frac{16 - x}{x} = \frac{15}{x + 1}$

$\Rightarrow \left( 16 - x \right)\left( x + 1 \right) = 15x$

$\Rightarrow 16x + 16 - x^2 - x = 15x$

$\Rightarrow - x^2 + 16 + 15x = 15x$

$\Rightarrow - x^2 + 16 = 0$

$\Rightarrow x^2 - 16 = 0$

$\Rightarrow \left( x - 4 \right)\left( x + 4 \right) = 0$

$\Rightarrow x - 4 = 0 \text { or } x + 4 = 0$

$\Rightarrow x = 4\text { or } x = - 4$

Hence, the factors are 4 and −4.

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#### APPEARS IN

Solution Solve the Following Quadratic Equations by Factorization: Concept: Solutions of Quadratic Equations by Factorization.
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