Algebra Examples

$\frac{3}{x} + \frac{6}{7 x^{2}}$

Step 1

To write $\frac{3}{x}$ as a fraction with a common denominator, multiply by $\frac{7 x}{7 x}$ .

$\frac{3}{x} \cdot \frac{7 x}{7 x} + \frac{6}{7 x^{2}}$

Step 2

Write each expression with a common denominator of $7 x^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{3}{x}$ by $\frac{7 x}{7 x}$ .

$\frac{3 (7 x)}{x (7 x)} + \frac{6}{7 x^{2}}$

Step 2.2

Rewrite using the commutative property of multiplication.

$\frac{3 (7 x)}{7 x \cdot x} + \frac{6}{7 x^{2}}$

Step 2.3

Multiply $x$ by $x$ by adding the exponents.

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Step 2.3.1

Move $x$ .

$\frac{3 (7 x)}{7 (x \cdot x)} + \frac{6}{7 x^{2}}$

Step 2.3.2

Multiply $x$ by $x$ .

$\frac{3 (7 x)}{7 x^{2}} + \frac{6}{7 x^{2}}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 (7 x) + 6}{7 x^{2}}$

Step 4

Factor $3$ out of $3 \cdot 7 x + 6$ .

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Step 4.1

Factor $3$ out of $6$ .

$\frac{3 (7 x) + 3 \cdot 2}{7 x^{2}}$

Step 4.2

Factor $3$ out of $3 (7 x) + 3 \cdot 2$ .

$\frac{3 (7 x + 2)}{7 x^{2}}$