Basic Math Examples

\frac{6}{p^{3} p^{3}} - \frac{6}{p^{4} q}

$\frac{6}{p^{3} p^{3}} - \frac{6}{p^{4} q}$

Step 1

Multiply

p^{3}

$p^{3}$ by

p^{3}

$p^{3}$ by adding the exponents.

Tap for more steps...

Step 1.1

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

\frac{6}{p^{3 + 3}} - \frac{6}{p^{4} q}

$\frac{6}{p^{3 + 3}} - \frac{6}{p^{4} q}$

Step 1.2

Add

3

$3$ and

3

$3$ .

\frac{6}{p^{6}} - \frac{6}{p^{4} q}

$\frac{6}{p^{6}} - \frac{6}{p^{4} q}$

\frac{6}{p^{6}} - \frac{6}{p^{4} q}

$\frac{6}{p^{6}} - \frac{6}{p^{4} q}$

Step 2

To write

\frac{6}{p^{6}}

$\frac{6}{p^{6}}$ as a fraction with a common denominator, multiply by

\frac{q}{q}

$\frac{q}{q}$ .

\frac{6}{p^{6}} \cdot \frac{q}{q} - \frac{6}{p^{4} q}

$\frac{6}{p^{6}} \cdot \frac{q}{q} - \frac{6}{p^{4} q}$

Step 3

To write

- \frac{6}{p^{4} q}

$- \frac{6}{p^{4} q}$ as a fraction with a common denominator, multiply by

\frac{p^{2}}{p^{2}}

$\frac{p^{2}}{p^{2}}$ .

\frac{6}{p^{6}} \cdot \frac{q}{q} - \frac{6}{p^{4} q} \cdot \frac{p^{2}}{p^{2}}

$\frac{6}{p^{6}} \cdot \frac{q}{q} - \frac{6}{p^{4} q} \cdot \frac{p^{2}}{p^{2}}$

Step 4

Write each expression with a common denominator of

q p^{6}

$q p^{6}$ , by multiplying each by an appropriate factor of

1

$1$ .

Tap for more steps...

Step 4.1

Multiply

\frac{6}{p^{6}}

$\frac{6}{p^{6}}$ by

\frac{q}{q}

$\frac{q}{q}$ .

\frac{6 q}{p^{6} q} - \frac{6}{p^{4} q} \cdot \frac{p^{2}}{p^{2}}

$\frac{6 q}{p^{6} q} - \frac{6}{p^{4} q} \cdot \frac{p^{2}}{p^{2}}$

Step 4.2

Multiply

\frac{6}{p^{4} q}

$\frac{6}{p^{4} q}$ by

\frac{p^{2}}{p^{2}}

$\frac{p^{2}}{p^{2}}$ .

\frac{6 q}{p^{6} q} - \frac{6 p^{2}}{p^{4} q p^{2}}

$\frac{6 q}{p^{6} q} - \frac{6 p^{2}}{p^{4} q p^{2}}$

Step 4.3

Multiply

p^{4}

$p^{4}$ by

p^{2}

$p^{2}$ by adding the exponents.

Tap for more steps...

Step 4.3.1

Move

p^{2}

$p^{2}$ .

\frac{6 q}{p^{6} q} - \frac{6 p^{2}}{p^{2} p^{4} q}

$\frac{6 q}{p^{6} q} - \frac{6 p^{2}}{p^{2} p^{4} q}$

Step 4.3.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

\frac{6 q}{p^{6} q} - \frac{6 p^{2}}{p^{2 + 4} q}

$\frac{6 q}{p^{6} q} - \frac{6 p^{2}}{p^{2 + 4} q}$

Step 4.3.3

Add

2

$2$ and

4

$4$ .

\frac{6 q}{p^{6} q} - \frac{6 p^{2}}{p^{6} q}

$\frac{6 q}{p^{6} q} - \frac{6 p^{2}}{p^{6} q}$

\frac{6 q}{p^{6} q} - \frac{6 p^{2}}{p^{6} q}

$\frac{6 q}{p^{6} q} - \frac{6 p^{2}}{p^{6} q}$

\frac{6 q}{p^{6} q} - \frac{6 p^{2}}{p^{6} q}

$\frac{6 q}{p^{6} q} - \frac{6 p^{2}}{p^{6} q}$

Step 5

Combine the numerators over the common denominator.

\frac{6 q - 6 p^{2}}{p^{6} q}

$\frac{6 q - 6 p^{2}}{p^{6} q}$

Step 6

Factor

6

$6$ out of

6 q - 6 p^{2}

$6 q - 6 p^{2}$ .

Tap for more steps...

Step 6.1

Factor

$6$ out of

$6 q$ .

$\frac{6 (q) - 6 p^{2}}{p^{6} q}$

Step 6.2

Factor

$6$ out of

$- 6 p^{2}$ .

$\frac{6 (q) + 6 (- p^{2})}{p^{6} q}$

Step 6.3

Factor

$6$ out of

$6 (q) + 6 (- p^{2})$ .

$\frac{6 (q - p^{2})}{p^{6} q}$