Precalculus Examples

$\frac{6}{7 p} - \frac{5}{2 p^{2}}$

Step 1

To write $\frac{6}{7 p}$ as a fraction with a common denominator, multiply by $\frac{2 p}{2 p}$ .

$\frac{6}{7 p} \cdot \frac{2 p}{2 p} - \frac{5}{2 p^{2}}$

Step 2

To write $- \frac{5}{2 p^{2}}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{6}{7 p} \cdot \frac{2 p}{2 p} - \frac{5}{2 p^{2}} \cdot \frac{7}{7}$

Step 3

Write each expression with a common denominator of $14 p^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{6}{7 p}$ by $\frac{2 p}{2 p}$ .

$\frac{6 (2 p)}{7 p (2 p)} - \frac{5}{2 p^{2}} \cdot \frac{7}{7}$

Step 3.2

Multiply $2$ by $7$ .

$\frac{6 (2 p)}{14 p \cdot p} - \frac{5}{2 p^{2}} \cdot \frac{7}{7}$

Step 3.3

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

$\frac{6 (2 p)}{14 (p^{1} p)} - \frac{5}{2 p^{2}} \cdot \frac{7}{7}$

Step 3.4

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

$\frac{6 (2 p)}{14 (p^{1} p^{1})} - \frac{5}{2 p^{2}} \cdot \frac{7}{7}$

Step 3.5

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

$\frac{6 (2 p)}{14 p^{1 + 1}} - \frac{5}{2 p^{2}} \cdot \frac{7}{7}$

Step 3.6

Add $1$ and $1$ .

$\frac{6 (2 p)}{14 p^{2}} - \frac{5}{2 p^{2}} \cdot \frac{7}{7}$

Step 3.7

Multiply $\frac{5}{2 p^{2}}$ by $\frac{7}{7}$ .

$\frac{6 (2 p)}{14 p^{2}} - \frac{5 \cdot 7}{2 p^{2} \cdot 7}$

Step 3.8

Multiply $7$ by $2$ .

$\frac{6 (2 p)}{14 p^{2}} - \frac{5 \cdot 7}{14 p^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{6 (2 p) - 5 \cdot 7}{14 p^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $6$ by $2$ .

$\frac{12 p - 5 \cdot 7}{14 p^{2}}$

Step 5.2

Multiply $- 5$ by $7$ .

$\frac{12 p - 35}{14 p^{2}}$