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Quadratic Equations — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsQuadratic Equations4 Marks
Question
Solve the following quadratic equations by factorization:
$\frac{\text{x}+1}{\text{x}-1}-\frac{\text{x}-1}{\text{x}+1}=\frac{5}{6},$ $\text{x}\neq1,-1$
✓

Answer

We have been given
$\frac{\text{x}+1}{\text{x}-1}-\frac{\text{x}-1}{\text{x}+1}=\frac{5}{6}$
$6(x^2 + 1 + 2x - x^2 - 1 + 2x) = 5(x^2 - 1)$
$5x^2 - 24x - 5 = 0$
$5x^2 - 25x + x - 5 = 0$
$5x(x - 5) + 1(x - 5) = 0$
$(5x + 1)(x - 5) = 0$
Therefore,
$5x + 1 = 0$
$5x = -1$
$​\text{x}=\frac{-1}{5}$
or,
$x - 5 = 0$
$x = 5$
Hence, $​\text{x}=\frac{-1}{5}$ or $x = 5$

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