Question

Find the root of the following equation....
$\frac{1}{x + 4} - \frac{1}{x -7 } = \frac{11}{30}$

Answer 1

$\frac{1}{x + 4} - \frac{1}{x -7 } = \frac{11}{30} \\ = > \frac{x - 7 - x - 4}{(x + 4)(x - 7)} = \frac{11}{30} \\ = > \frac{ - 11}{ ({x}^{2} - 7x + 4x - 28 )} = \frac{11}{30} \\ = > \frac{ - 1}{ ({x}^{2} - 3x - 28) } = \frac{1}{30} ....multiplying \: both \: side \: by( \frac{1}{11} )\\ = > - 30 = {x}^{2} - 3x - 28 \\ = > {x}^{2} - 3x - 28 + 30 \\ = > {x}^{2} - 3x + 2 = 0 \\ = > {x}^{2} - 2x - x + 2 = 0 \\ = > x(x - 2) - 1(x - 2) = 0 \\ = > (x - 1)(x - 2) \\ \\ x = 1 \: orx = 2$
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Answer 2

Hello !!
see this answer.☺☺