What is x/(x+2)-x/(x-2) ?

The solution to x/(x+2)-x/(x-2) is -(4x)/((x+2)(x-2))

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simplify x/(x+2)-x/(x-2)

simplify

\frac{x}{x + 2} - \frac{x}{x - 2}

- \frac{4 x}{( x + 2 ) ( x - 2 )}

Solution steps

\frac{x}{x + 2} - \frac{x}{x - 2}

Least Common Multiplier of

x + 2, x - 2 : (x + 2) (x - 2)

Adjust Fractions based on the LCM

= \frac{x ( x - 2 )}{( x + 2 ) ( x - 2 )} - \frac{x ( x + 2 )}{( x + 2 ) ( x - 2 )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{x ( x - 2 ) - x ( x + 2 )}{( x + 2 ) ( x - 2 )}

Simplify

x (x - 2) - x (x + 2) : - 4 x

= \frac{- 4 x}{( x + 2 ) ( x - 2 )}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{4 x}{( x + 2 ) ( x - 2 )}

\frac{3}{2} \times (- 3)

x^{3} - 12 x^{2} + 256

e^{- 2 l n (x) + c}

- \frac{2}{3} \times 4

- \frac{2}{3} \times 5