Question

$\frac{1}{x - 5} - \frac{1}{x - 3} + \frac{1}{x + 5} - \frac{1}{x + 3}$
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Answer 1

Step-by-step explanation:

Dekho isse aise krte hai (solve)

$\frac{1}{x - 5} - \frac{1}{x - 3} + \frac{1}{x + 5} - \frac{1}{x + 3} \\ \\ \frac{x - 3 - x + 5}{(x - 5)(x - 3)} + \frac{x + 3 - x - 5}{(x + 5)(x + 3)} \\ \\ \frac{2}{(x - 5)(x - 3)} - \frac{2}{(x + 5)(x + 3)} \\ \\ \frac{2(x + 5)(x + 3) - 2(x - 5)(x - 3}{ ({x}^{2} - 25)( {x}^{2} - 9)} \\ \\ \frac{2( {x}^{2} + 8x + 15) - 2( {x}^{2} - 8x + 15) }{( {x}^{2} - 25)( {x}^{2} - 9)} \\ \\ \frac{16x + 30 + 16x - 30}{ {x}^{4} - 34 {x}^{2} + 225} \\ \\ \\ \boxed{ \boxed{ \frac{32x}{ {x}^{4} - 34 {x}^{2} + 225 } }}$