Algebra Examples

$\frac{4}{7 x^{2}} - \frac{3}{2 x^{3}}$

Step 1

To write $\frac{4}{7 x^{2}}$ as a fraction with a common denominator, multiply by $\frac{2 x}{2 x}$ .

$\frac{4}{7 x^{2}} \cdot \frac{2 x}{2 x} - \frac{3}{2 x^{3}}$

Step 2

To write $- \frac{3}{2 x^{3}}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{4}{7 x^{2}} \cdot \frac{2 x}{2 x} - \frac{3}{2 x^{3}} \cdot \frac{7}{7}$

Step 3

Write each expression with a common denominator of $14 x^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{4}{7 x^{2}}$ by $\frac{2 x}{2 x}$ .

$\frac{4 (2 x)}{7 x^{2} (2 x)} - \frac{3}{2 x^{3}} \cdot \frac{7}{7}$

Step 3.2

Multiply $2$ by $7$ .

$\frac{4 (2 x)}{14 x^{2} x} - \frac{3}{2 x^{3}} \cdot \frac{7}{7}$

Step 3.3

Raise $x$ to the power of $1$ .

$\frac{4 (2 x)}{14 (x^{1} x^{2})} - \frac{3}{2 x^{3}} \cdot \frac{7}{7}$

Step 3.4

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

$\frac{4 (2 x)}{14 x^{1 + 2}} - \frac{3}{2 x^{3}} \cdot \frac{7}{7}$

Step 3.5

Add $1$ and $2$ .

$\frac{4 (2 x)}{14 x^{3}} - \frac{3}{2 x^{3}} \cdot \frac{7}{7}$

Step 3.6

Multiply $\frac{3}{2 x^{3}}$ by $\frac{7}{7}$ .

$\frac{4 (2 x)}{14 x^{3}} - \frac{3 \cdot 7}{2 x^{3} \cdot 7}$

Step 3.7

Multiply $7$ by $2$ .

$\frac{4 (2 x)}{14 x^{3}} - \frac{3 \cdot 7}{14 x^{3}}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 (2 x) - 3 \cdot 7}{14 x^{3}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $4$ by $2$ .

$\frac{8 x - 3 \cdot 7}{14 x^{3}}$

Step 5.2

Multiply $- 3$ by $7$ .

$\frac{8 x - 21}{14 x^{3}}$