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

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

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simplify x/(a^2-ax)+1/a+1/x

simplify

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

\frac{a}{x ( - x + a )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

Cancel

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

= \frac{a}{x ( - x + a )}

∣ 15 ∣

\frac{4}{6 - 2}

3 x (x - 3)

3 x (x + 5)

(x - 2 a)^{3}