Basic Math Examples

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

Step 1

To write $2$ as a fraction with a common denominator, multiply by $\frac{a b}{a b}$ .

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

Step 2

Simplify terms.

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Step 2.1

Combine $2$ and $\frac{a b}{a b}$ .

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 3

Factor using the perfect square rule.

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Step 3.1

Rearrange terms.

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

Step 3.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 a b = 2 \cdot a \cdot b$

Step 3.3

Rewrite the polynomial.

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

Step 3.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = a$ and $b = b$ .

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