Simplify (a^2+b^2)/(a-b)-a

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

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

$\frac{a^{2} + b^{2}}{a - b} - a \cdot \frac{a - b}{a - b}$

Simplify terms.

Combine $- a$ and $\frac{a - b}{a - b}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

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

Multiply $a$ by $a$ .

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

Rewrite using the commutative property of multiplication.

$\frac{a^{2} + b^{2} - a^{2} - 1 \cdot - 1 a b}{a - b}$

Simplify each term.

Multiply $- 1$ by $- 1$ .

$\frac{a^{2} + b^{2} - a^{2} + 1 a b}{a - b}$

Multiply $a$ by $1$ .

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

Subtract $a^{2}$ from $a^{2}$ .

$\frac{b^{2} + 0 + a b}{a - b}$

Add $b^{2}$ and $0$ .

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

Factor $b$ out of $b^{2} + a b$ .

Factor $b$ out of $b^{2}$ .

$\frac{b \cdot b + a b}{a - b}$

Factor $b$ out of $a b$ .

$\frac{b \cdot b + b a}{a - b}$

Factor $b$ out of $b \cdot b + b a$ .

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