What is x/(x+5)+(10x)/(x^2-25) ?

The solution to x/(x+5)+(10x)/(x^2-25) is x/(x-5)

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simplify x/(x+5)+(10x)/(x^2-25)

simplify

\frac{x}{x + 5} + \frac{10 x}{x ^{2} - 25}

\frac{x}{x - 5}

Solution steps

\frac{x}{x + 5} + \frac{10 x}{x ^{2} - 25}

Least Common Multiplier of

x + 5, x^{2} - 25 : (x + 5) (x - 5)

Adjust Fractions based on the LCM

= \frac{x ( x - 5 )}{( x + 5 ) ( x - 5 )} + \frac{10 x}{( x + 5 ) ( x - 5 )}

Apply the fraction rule:

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

= \frac{x ( x - 5 ) + 10 x}{( x + 5 ) ( x - 5 )}

Simplify

x (x - 5) + 10 x : x^{2} + 5 x

= \frac{x ^{2} + 5 x}{( x + 5 ) ( x - 5 )}

Cancel

\frac{x ^{2} + 5 x}{( x + 5 ) ( x - 5 )} : \frac{x}{x - 5}

= \frac{x}{x - 5}

cos^{2} (x) csc (x) sec (x)

- (x - 7 y) - 2 (2 y - 5 x)

\frac{\frac{15 - 3 x}{x + 5}}{\frac{5 x - x ^{2}}{5 x + 1}}

What is x/(x+5)+(10x)/(x^2-25) ?
The solution to x/(x+5)+(10x)/(x^2-25) is x/(x-5)