Question

Question :

$\frac{1}{x-1}-\frac{1}{x+5} = \frac{6}{7} , x \ne 1,-5$

Answer

Answer 1

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Answer 2

$\huge{\bold{Answer:}}$

$\sf \frac{1}{x - 1} - \frac{1}{x + 5} = \frac{6}{7} \\ \\\sf \frac{(x + 5) - (x - 1)}{(x - 1)(x + 5)} = \frac{6}{7} \\ \\ \sf \frac{x + 5 - x + 1}{x {}^{2} + 5x - x - 5} = \frac{6}{7} \\ \\\sf \frac{6}{x {}^{2} + 4x - 5} = \frac{6}{7} \\ \\\bf on \: cross - multiplying : \\ \\\sf 6(x {}^{2} + 4x - 5) = 6 \times 7 \\ \\\sf x {}^{2} + 4x - 5 = 7 \\ \\ \sf x {}^{2} + 4x - 5 - 7 = 0 \\ \\ \sf x {}^{2} + 4x - 12 = 0 \\ \\ \bf on \: splitting \: its \: middle \: term :$

$\sf x {}^{2} + 6x - 2x - 12 = 0 \\ \\ \sf x(x + 6) - 2(x + 6) = 0 \\ \\ \sf (x + 6)(x - 2) = 0 \\ \\ \sf \left \{ {{x = - 6} \atop {x= \: 2}} \right.$

Thanks for the question!