Algebra Examples

$\frac{1}{3 x^{2}} + \frac{1}{9 x^{4}}$

Step 1

To write $\frac{1}{3 x^{2}}$ as a fraction with a common denominator, multiply by $\frac{3 x^{2}}{3 x^{2}}$ .

$\frac{1}{3 x^{2}} \cdot \frac{3 x^{2}}{3 x^{2}} + \frac{1}{9 x^{4}}$

Step 2

Write each expression with a common denominator of $9 x^{4}$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{1}{3 x^{2}}$ by $\frac{3 x^{2}}{3 x^{2}}$ .

$\frac{3 x^{2}}{3 x^{2} (3 x^{2})} + \frac{1}{9 x^{4}}$

Step 2.2

Rewrite using the commutative property of multiplication.

$\frac{3 x^{2}}{3 \cdot 3 x^{2} x^{2}} + \frac{1}{9 x^{4}}$

Step 2.3

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 2.3.1

Move $x^{2}$ .

$\frac{3 x^{2}}{3 \cdot 3 (x^{2} x^{2})} + \frac{1}{9 x^{4}}$

Step 2.3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 x^{2}}{3 \cdot 3 x^{2 + 2}} + \frac{1}{9 x^{4}}$

Step 2.3.3

Add $2$ and $2$ .

$\frac{3 x^{2}}{3 \cdot 3 x^{4}} + \frac{1}{9 x^{4}}$

Step 2.4

Multiply $3$ by $3$ .

$\frac{3 x^{2}}{9 x^{4}} + \frac{1}{9 x^{4}}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 x^{2} + 1}{9 x^{4}}$