Basic Math Examples

$\frac{u}{8 a^{2} c} - \frac{5 a^{3} w}{12 c^{2} k}$

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

Multiply $\frac{u}{8 a^{2} c}$ by $\frac{3 k c}{3 k c}$ .

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

Step 3.2

Multiply $3$ by $8$ .

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

Step 3.3

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

$\frac{u (3 k c)}{24 a^{2} (c^{1} c) k} - \frac{5 a^{3} w}{12 c^{2} k} \cdot \frac{2 a^{2}}{2 a^{2}}$

Step 3.4

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

$\frac{u (3 k c)}{24 a^{2} (c^{1} c^{1}) k} - \frac{5 a^{3} w}{12 c^{2} k} \cdot \frac{2 a^{2}}{2 a^{2}}$

Step 3.5

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

$\frac{u (3 k c)}{24 a^{2} c^{1 + 1} k} - \frac{5 a^{3} w}{12 c^{2} k} \cdot \frac{2 a^{2}}{2 a^{2}}$

Step 3.6

Add $1$ and $1$ .

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

Step 3.7

Multiply $\frac{5 a^{3} w}{12 c^{2} k}$ by $\frac{2 a^{2}}{2 a^{2}}$ .

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

Step 3.8

Multiply $2$ by $12$ .

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

Step 3.9

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Move $3$ to the left of $u$ .

$\frac{3 \cdot u k c - 5 a^{3} w (2 a^{2})}{24 a^{2} c^{2} k}$

Step 5.2

Multiply $a^{3}$ by $a^{2}$ by adding the exponents.

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Step 5.2.1

Move $a^{2}$ .

$\frac{3 u k c - 5 (a^{2} a^{3}) w \cdot 2}{24 a^{2} c^{2} k}$

Step 5.2.2

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

$\frac{3 u k c - 5 a^{2 + 3} w \cdot 2}{24 a^{2} c^{2} k}$

Step 5.2.3

Add $2$ and $3$ .

$\frac{3 u k c - 5 a^{5} w \cdot 2}{24 a^{2} c^{2} k}$

Step 5.3

Multiply $2$ by $- 5$ .

$\frac{3 u k c - 10 a^{5} w}{24 a^{2} c^{2} k}$