What is (4x)/(x^2-4)+x/(x+2) ?

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

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simplify (4x)/(x^2-4)+x/(x+2)

simplify

\frac{4 x}{x ^{2} - 4} + \frac{x}{x + 2}

\frac{x}{x - 2}

Solution steps

\frac{4 x}{x ^{2} - 4} + \frac{x}{x + 2}

Least Common Multiplier of

x^{2} - 4, x + 2 : (x + 2) (x - 2)

Adjust Fractions based on the LCM

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

Simplify

4 x + x (x - 2) : x^{2} + 2 x

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

Cancel

\frac{x ^{2} + 2 x}{( x + 2 ) ( x - 2 )} : \frac{x}{x - 2}

= \frac{x}{x - 2}

(\frac{1}{8} a - \frac{3}{4} b)^{2}

\frac{2}{3} \div \frac{1}{9}

\frac{7}{9} + \frac{1}{15}

5 x + 3 - (2 x - 7)

(- 2 \cdot 15)^{2}