Question

solve 1/(x+5) + 1/(x+4) = 1/(x+2) +1/(x+7)

Answer 1

$\huge\boxed{\fcolorbox{white}{pink}{answer}}$

Here is ur answer mate

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$\frac{1}{x + 5} + \frac{1}{x + 4} = \frac{1}{x + 2} + \frac{1}{x + 7} \\ \frac{(x + 4) + (x + 5)}{(x + 5)(x + 4)} = \frac{(x + 7) + (x + 2)}{(x + 2)(x + 7)} \\ \frac{2x + 9}{x {}^{2} + 9x + 20 } = \frac{2x + 9}{x {}^{2} + 9x + 14 } \\ (2x + 9)(x {}^{2} + 9x + 14) = (2x + 9)(x {}^{2} + 9x + 20) \\ 2x {}^{3} + 18x {}^{2} + 28x + 9x {}^{2} + 81x + 126 = 2x {}^{3} + 18x {}^{2} + 40x + 9x {}^{2} + 81x + 180 \\ 28x + 126 = 40x + 180 \\ 28x - 40x = 180 - 126 \\ - 12x = 54 \\ x = - \frac{54}{12} \\ x = - \frac{27}{6}$

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