What is x/(x^2-4)+1/x ?

The solution to x/(x^2-4)+1/x is (2x^2-4)/(x(x+2)(x-2))

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simplify x/(x^2-4)+1/x

simplify

\frac{x}{x ^{2} - 4} + \frac{1}{x}

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

Solution steps

\frac{x}{x ^{2} - 4} + \frac{1}{x}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

4 x^{2} - 20

107 - (- 25)

\frac{x ^{3} + 8}{x ^{2} - 4}

8 + 6 x^{4}

(- 10 c^{4}) (- 3 c^{4})