Simplify (a^2)/(ax-x^2)+x/(x-a)

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

Factor $x$ out of $a x - x^{2}$ .

Factor $x$ out of $a x$ .

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

Factor $x$ out of $- x^{2}$ .

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

Factor $x$ out of $x a + x (- x)$ .

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

Factor $- 1$ out of $x$ .

$\frac{a^{2}}{x (a - x)} + \frac{x}{- 1 (- x) - a}$

Factor $- 1$ out of $- a$ .

$\frac{a^{2}}{x (a - x)} + \frac{x}{- 1 (- x) - (a)}$

Factor $- 1$ out of $- 1 (- x) - (a)$ .

$\frac{a^{2}}{x (a - x)} + \frac{x}{- 1 (- x + a)}$

Simplify the expression.

Move a negative from the denominator of $\frac{x}{- 1 (- x + a)}$ to the numerator.

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

Reorder terms.

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

To write $\frac{- x}{a - x}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

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

Write each expression with a common denominator of $x (a - x)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{- x}{a - x}$ by $\frac{x}{x}$ .

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

Reorder the factors of $(a - x) x$ .

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

Combine the numerators over the common denominator.

$\frac{a^{2} - x \cdot x}{x (a - x)}$

Simplify the numerator.

Rewrite $x \cdot x$ as $x^{2}$ .

$\frac{a^{2} - x^{2}}{x (a - x)}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = x$ .

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

Cancel the common factor of $a - x$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{a + x}{x}$