9x 1 2x 3=5x+1⇒9(x 3) 2(x 1)(x 1)(x )=5x+1 ⇒ (9x 27 2x+2)(x+1)=5(x 1)(x 3) ⇒ (7x 25)(x+1)=5(x 1)(x 3) ⇒ 7x^2 25x+7x 25=5(x^2+3 4x) ⇒ 7x^2 1 ...

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Solving Using Quadratic Formula When D>0

Solve 9x-1-2...

Question

Solve
$\frac{9}{x - 1} - \frac{2}{x - 3} = \frac{5}{x + 1}$

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Solution

$\frac{9}{x - 1} - \frac{2}{x - 3} = \frac{5}{x + 1} \Rightarrow \frac{9 (x - 3) - 2 (x - 1)}{(x - 1) (x -)} = \frac{5}{x + 1} \Rightarrow (9 x - 27 - 2 x + 2) (x + 1) = 5 (x - 1) (x - 3) \Rightarrow (7 x - 25) (x + 1) = 5 (x - 1) (x - 3) \Rightarrow 7 x^{2} - 25 x + 7 x - 25 = 5 (x^{2} + 3 - 4 x) \Rightarrow 7 x^{2} - 18 x - 25 = 5 x^{2} + 15 - 20 x \Rightarrow 2 x + 2 x - 1 == 0 x^{2} + x - 5 = 0 \Rightarrow x = \frac{- 1 \pm \sqrt{1 + 20}}{2} = \frac{- 1 \pm \sqrt{21}}{2} x = \frac{- 1 \pm \sqrt{21}}{2}$

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