Question

5/(x+2)-3/(x-2) =3/x​

Answer 1

$\huge\mathcal\colorbox{skyblue}{\color{black}{AnSwEr~↓~↓~}}$

$\bf \frac{5}{x + 2} - \frac{3}{x - 2} = \frac{3}{x} \\ \\ \bf \frac{5(x - 2) - 3(x + 2)}{(x + 2)(x - 2)} = \frac{3}{x} \\ \\ \bf \frac{5x - 10 - 3x - 6}{ {x}^{2} - {2}^{2} } = \frac{3}{x} \\ \\ \bf \frac{2x - 16}{ {x}^{2} - 4 } = \frac{3}{x} \\ \\ \bf by \: cross \: multiplication \: we \: get : \\ \\ \bf x(2x - 16) = 3( {x}^{2} - 4) \\ \bf 2 {x}^{2} - 16x = {3x}^{2} - 12 \\ \bf {2x}^{2} - {3x}^{2} - 16x = - 12 \\ \bf - {x}^{2} - 16x = - 12 \\ \bf - x(x + 16) = - 12 \\ \bf x + 16 = \frac{ - 12}{ - x} \\ \bf x + 16 = \frac{12}{x} \\ \blue{ \underline{ \boxed{ \bf \: x - \frac{12}{x} = - 16 \: }}}$

$\huge\blue{\textbf{\textsf{Hope~it~helps..!!}}}$