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Multiplication of Any Polynomial

Solve: 3x+1...

Question

Solve: $\frac{3 x + 1}{2} - \frac{4}{x - 1} = x + 2$

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Solution

$\frac{3 x + 1}{2} - \frac{4}{x - 1} = x + 2$

$\Rightarrow \frac{(3 x + 1) (x - 1) - 8}{2 (x - 1)} = x + 2$

$\Rightarrow (3 x + 1) (x - 1) - 8 = 2 (x + 2) (x - 1)$

$\Rightarrow 3 x^{2} - 3 x + x - 1 - 8 = 2 [x^{2} - x + 2 x - 2]$

$\Rightarrow 3 x^{2} - 2 x - 9 = 2 x^{2} - 2 x + 4 x - 4$

$\Rightarrow 3 x^{2} - 2 x - 9 = 2 x^{2} + 2 x - 4$

$\Rightarrow 3 x^{2} - 2 x - 9 - 2 x^{2} - 2 x + 4 = 0$

$\Rightarrow x^{2} - 4 x - 5 = 0$

$\Rightarrow x^{2} - 5 x + x - 5 = 0$

$\Rightarrow x (x - 5) + 1 (x - 5) = 0$

$\Rightarrow (x - 5) (x + 1) = 0$

$∴ x = 5, - 1$

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{lim}_{x \to 1} \frac{x^{4} - {3 x}^{3} + 2}{x^{3} - {5 x}^{2} + 3 x + 1}

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