Basic Math Examples

$\frac{3 v}{8 d^{3} k^{2}} - \frac{5 d^{3} u}{12 a^{2} k}$

Step 1

To write $\frac{3 v}{8 d^{3} k^{2}}$ as a fraction with a common denominator, multiply by $\frac{3 a^{2}}{3 a^{2}}$ .

$\frac{3 v}{8 d^{3} k^{2}} \cdot \frac{3 a^{2}}{3 a^{2}} - \frac{5 d^{3} u}{12 a^{2} k}$

Step 2

To write $- \frac{5 d^{3} u}{12 a^{2} k}$ as a fraction with a common denominator, multiply by $\frac{2 d^{3} k}{2 d^{3} k}$ .

$\frac{3 v}{8 d^{3} k^{2}} \cdot \frac{3 a^{2}}{3 a^{2}} - \frac{5 d^{3} u}{12 a^{2} k} \cdot \frac{2 d^{3} k}{2 d^{3} k}$

Step 3

Write each expression with a common denominator of $24 d^{3} k^{2} a^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3 v}{8 d^{3} k^{2}}$ by $\frac{3 a^{2}}{3 a^{2}}$ .

$\frac{3 v (3 a^{2})}{8 d^{3} k^{2} (3 a^{2})} - \frac{5 d^{3} u}{12 a^{2} k} \cdot \frac{2 d^{3} k}{2 d^{3} k}$

Step 3.2

Multiply $3$ by $8$ .

$\frac{3 v (3 a^{2})}{24 d^{3} k^{2} a^{2}} - \frac{5 d^{3} u}{12 a^{2} k} \cdot \frac{2 d^{3} k}{2 d^{3} k}$

Step 3.3

Multiply $\frac{5 d^{3} u}{12 a^{2} k}$ by $\frac{2 d^{3} k}{2 d^{3} k}$ .

$\frac{3 v (3 a^{2})}{24 d^{3} k^{2} a^{2}} - \frac{5 d^{3} u (2 d^{3} k)}{12 a^{2} k (2 d^{3} k)}$

Step 3.4

Multiply $2$ by $12$ .

$\frac{3 v (3 a^{2})}{24 d^{3} k^{2} a^{2}} - \frac{5 d^{3} u (2 d^{3} k)}{24 a^{2} k (d^{3} k)}$

Step 3.5

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

$\frac{3 v (3 a^{2})}{24 d^{3} k^{2} a^{2}} - \frac{5 d^{3} u (2 d^{3} k)}{24 a^{2} (d^{3} (k^{1} k))}$

Step 3.6

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

$\frac{3 v (3 a^{2})}{24 d^{3} k^{2} a^{2}} - \frac{5 d^{3} u (2 d^{3} k)}{24 a^{2} (d^{3} (k^{1} k^{1}))}$

Step 3.7

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

$\frac{3 v (3 a^{2})}{24 d^{3} k^{2} a^{2}} - \frac{5 d^{3} u (2 d^{3} k)}{24 a^{2} (d^{3} k^{1 + 1})}$

Step 3.8

Add $1$ and $1$ .

$\frac{3 v (3 a^{2})}{24 d^{3} k^{2} a^{2}} - \frac{5 d^{3} u (2 d^{3} k)}{24 a^{2} (d^{3} k^{2})}$

Step 3.9

Reorder the factors of $24 d^{3} k^{2} a^{2}$ .

$\frac{3 v (3 a^{2})}{24 d^{3} a^{2} k^{2}} - \frac{5 d^{3} u (2 d^{3} k)}{24 a^{2} (d^{3} k^{2})}$

Step 3.10

Reorder the factors of $24 a^{2} (d^{3} k^{2})$ .

$\frac{3 v (3 a^{2})}{24 d^{3} a^{2} k^{2}} - \frac{5 d^{3} u (2 d^{3} k)}{24 d^{3} a^{2} k^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 v (3 a^{2}) - 5 d^{3} u (2 d^{3} k)}{24 d^{3} a^{2} k^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $3$ .

$\frac{9 v a^{2} - 5 d^{3} u (2 d^{3} k)}{24 d^{3} a^{2} k^{2}}$

Step 5.2

Multiply $d^{3}$ by $d^{3}$ by adding the exponents.

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Step 5.2.1

Move $d^{3}$ .

$\frac{9 v a^{2} - 5 (d^{3} d^{3}) u (2 k)}{24 d^{3} a^{2} k^{2}}$

Step 5.2.2

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

$\frac{9 v a^{2} - 5 d^{3 + 3} u (2 k)}{24 d^{3} a^{2} k^{2}}$

Step 5.2.3

Add $3$ and $3$ .

$\frac{9 v a^{2} - 5 d^{6} u (2 k)}{24 d^{3} a^{2} k^{2}}$

Step 5.3

Multiply $2$ by $- 5$ .

$\frac{9 v a^{2} - 10 d^{6} u k}{24 d^{3} a^{2} k^{2}}$