Simplify 2/(15x)-4/(21x^2)

$\frac{2}{15 x} - \frac{4}{21 x^{2}}$

Step 1

To write $\frac{2}{15 x}$ as a fraction with a common denominator, multiply by $\frac{7 x}{7 x}$ .

$\frac{2}{15 x} \cdot \frac{7 x}{7 x} - \frac{4}{21 x^{2}}$

Step 2

To write $- \frac{4}{21 x^{2}}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2}{15 x} \cdot \frac{7 x}{7 x} - \frac{4}{21 x^{2}} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $105 x^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{15 x}$ by $\frac{7 x}{7 x}$ .

$\frac{2 (7 x)}{15 x (7 x)} - \frac{4}{21 x^{2}} \cdot \frac{5}{5}$

Multiply $7$ by $15$ .

$\frac{2 (7 x)}{105 x \cdot x} - \frac{4}{21 x^{2}} \cdot \frac{5}{5}$

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

$\frac{2 (7 x)}{105 (x^{1} x)} - \frac{4}{21 x^{2}} \cdot \frac{5}{5}$

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

$\frac{2 (7 x)}{105 (x^{1} x^{1})} - \frac{4}{21 x^{2}} \cdot \frac{5}{5}$

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

$\frac{2 (7 x)}{105 x^{1 + 1}} - \frac{4}{21 x^{2}} \cdot \frac{5}{5}$

Add $1$ and $1$ .

$\frac{2 (7 x)}{105 x^{2}} - \frac{4}{21 x^{2}} \cdot \frac{5}{5}$

Multiply $\frac{4}{21 x^{2}}$ by $\frac{5}{5}$ .

$\frac{2 (7 x)}{105 x^{2}} - \frac{4 \cdot 5}{21 x^{2} \cdot 5}$

Multiply $5$ by $21$ .

$\frac{2 (7 x)}{105 x^{2}} - \frac{4 \cdot 5}{105 x^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 (7 x) - 4 \cdot 5}{105 x^{2}}$

Step 5

Simplify the numerator.

Factor $2$ out of $2 \cdot 7 x - 4 \cdot 5$ .

Factor $2$ out of $2 \cdot 7 x$ .

$\frac{2 (7 x) - 4 \cdot 5}{105 x^{2}}$

Factor $2$ out of $- 4 \cdot 5$ .

$\frac{2 (7 x) + 2 (- 2 \cdot 5)}{105 x^{2}}$

Factor $2$ out of $2 (7 x) + 2 (- 2 \cdot 5)$ .

$\frac{2 (7 x - 2 \cdot 5)}{105 x^{2}}$

Multiply $- 2$ by $5$ .

$\frac{2 (7 x - 10)}{105 x^{2}}$