Solve equation, given below, using factorisation method:

$\frac{5}{x - 2} - \frac{3}{x + 6} = \frac{4}{x}$

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Solution

$\frac{5}{x - 2} - \frac{3}{x + 6} = \frac{4}{x} \Rightarrow \frac{5 (x + 6) - 3 (x - 2)}{(x - 2) (x + 6)} = \frac{4}{x} \Rightarrow \frac{5 x + 30 - 3 x + 6}{x^{2} + 4 x - 12} = \frac{4}{x} \Rightarrow \frac{2 x + 36}{x^{2} + 4 x - 12} = \frac{4}{x} \Rightarrow 2 x^{2} + 36 x = 4 x^{2} + 16 x - 48 \Rightarrow 2 x^{2} - 20 x - 48 = 0 \Rightarrow x^{2} - 10 x - 24 = 0 \Rightarrow x^{2} - 12 x + 2 x - 24 = 0 \Rightarrow x (x - 12) + 2 (x - 12) = 0 \Rightarrow (x - 12) (x + 2) = 0 \Rightarrow x = 12 o r x = - 2$

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