Algebra Examples

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

Step 1

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

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

Step 2

Simplify terms.

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Step 2.1

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

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 3

Simplify the numerator.

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Step 3.1

Apply the distributive property.

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

Step 3.2

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

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Step 3.2.1

Move $a$ .

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

Step 3.2.2

Multiply $a$ by $a$ .

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

Step 3.3

Rewrite using the commutative property of multiplication.

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

Step 3.4

Simplify each term.

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Step 3.4.1

Multiply $- 1$ by $- 1$ .

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

Step 3.4.2

Multiply $a$ by $1$ .

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

Step 3.5

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

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

Step 3.6

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

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

Step 3.7

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

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Step 3.7.1

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

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

Step 3.7.2

Factor $b$ out of $a b$ .

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

Step 3.7.3

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

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