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Quadratic Equations — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsQuadratic Equations5 Marks
Question
Solve the following quadratic equation:
$\frac{\text{1}}{\text{x}+1}+\frac{\text{2}}{\text{x}+2}=\frac{5}{\text{x}+4},$ $\text{x}\neq-1,-2,-4$
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Answer

$\frac{\text{1}}{\text{x}+1}+\frac{\text{2}}{\text{x}+2}=\frac{5}{\text{x}+4}$
$\Rightarrow\frac{\text{x}+2+\text{2x}+2}{(\text{x}+1)(\text{x}+2)}=\frac{5}{\text{x}+4}$
$\Rightarrow\frac{\text{3x}+4}{\text{x}^2+\text{3x}+2}=\frac{5}{\text{x}+4}$
$\Rightarrow (3x + 4)(x + 4) = 5(x^2 + 3x + 2)$
$\Rightarrow 3x^2 + 16x + 16 = 5x^2 + 15x + 10$
$\Rightarrow 2x^2 - x - 6 = 0$
$\Rightarrow 2x^2 - 4x + 3x - 6 = 0$
$\Rightarrow 2x(x - 2) + 3(x - 2) = 0$
$\Rightarrow (x - 2)(2x + 3) = 0$
$\Rightarrow x - 2 = 0$ or $2x + 3 = 0$
$\Rightarrow x = 2$ or $\text{x}=\frac{-3}{2}$

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