Solve the following quadratic equation by completing the square: $\frac{5 x + 7}{x - 1} = 3 x + 2$

{- 1, 3}

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{1, 3}

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{- 1, - 3}

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None of these

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Solution

The correct option is A ${- 1, 3}$
Given $\frac{5 x + 7}{x - 1} = 3 x + 2$

$\Rightarrow$ $5 x + 7 = (3 x + 2) (x - 1)$

$\Rightarrow$ $5 x + 7 = 3 x^{2} - 3 x + 2 x - 2$

$\Rightarrow$ $3 x^{2} - 6 x - 9 = 0$

$\Rightarrow$ $x^{2} - 2 x - 3 = 0$

$\Rightarrow$ Here, $a = 1, b = - 2, c = - 3$

$\Rightarrow$ $x^{2} - 2 x = 3$

Now, ${(\frac{b}{2})}^{2} = {(\frac{- 2}{2})}^{2} = 1$

Adding $1$ on both sides,

$\Rightarrow$ $x^{2} - 2 x + 1 = 3 + 1$

$\Rightarrow$ $(x - 1)^{2} = 4$

Taking square root on both sides

$\Rightarrow$ $x - 1 = \pm 2$

$\Rightarrow$ $x - 1 = 2$ and $x - 1 = - 2$

$∴$ $x = 3$ and $x = - 1$

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