What is x/(x-5)+(x-5)/x ?

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

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simplify x/(x-5)+(x-5)/x

simplify

\frac{x}{x - 5} + \frac{x - 5}{x}

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

Solution steps

\frac{x}{x - 5} + \frac{x - 5}{x}

Least Common Multiplier of

x - 5, x : x (x - 5)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x^{2} + (x - 5)^{2} : 2 x^{2} - 10 x + 25

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

\frac{sec ^{2} ( x ) - 1}{sin ^{2} ( x )}

6 + x - 17

- \frac{1}{4} + \frac{3}{5} - \frac{1}{3} - \frac{2}{6}

sin^{2} (x) - sin (x)

\frac{11}{3}

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