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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

(x - 4) (x + 2) + 4 x : x^{2} + 2 x - 8

= \frac{x ^{2} + 2 x - 8}{x ( x - 2 ) ( x + 2 )}

Cancel

\frac{x ^{2} + 2 x - 8}{x ( x - 2 ) ( x + 2 )} : \frac{x + 4}{x ( x + 2 )}

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

(- 7 x^{4} + 2 x - 3 x^{2} + x^{3}) - (5 - 2 x^{3} + 7 x + 2 x^{2} - 5)

4 \times (- 4)

(4 p - 1)^{2}

\frac{x}{x ^{6}}

(- \frac{3}{2})^{4}

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