Basic Math Examples

$\frac{5 u^{2}}{2 d k} - \frac{k^{3} y^{3}}{6 c^{3} d^{3}}$

Step 1

To write

$\frac{5 u^{2}}{2 d k}$ as a fraction with a common denominator, multiply by

$\frac{3 d^{2} c^{3}}{3 d^{2} c^{3}}$ .

$\frac{5 u^{2}}{2 d k} \cdot \frac{3 d^{2} c^{3}}{3 d^{2} c^{3}} - \frac{k^{3} y^{3}}{6 c^{3} d^{3}}$

Step 2

To write

$- \frac{k^{3} y^{3}}{6 c^{3} d^{3}}$ as a fraction with a common denominator, multiply by

$\frac{k}{k}$ .

$\frac{5 u^{2}}{2 d k} \cdot \frac{3 d^{2} c^{3}}{3 d^{2} c^{3}} - \frac{k^{3} y^{3}}{6 c^{3} d^{3}} \cdot \frac{k}{k}$

Step 3

Write each expression with a common denominator of

$6 k d^{3} c^{3}$ , by multiplying each by an appropriate factor of

$1$ .

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Step 3.1

Multiply

$\frac{5 u^{2}}{2 d k}$ by

$\frac{3 d^{2} c^{3}}{3 d^{2} c^{3}}$ .

$\frac{5 u^{2} (3 d^{2} c^{3})}{2 d k (3 d^{2} c^{3})} - \frac{k^{3} y^{3}}{6 c^{3} d^{3}} \cdot \frac{k}{k}$

Step 3.2

Multiply

$3$ by

$2$ .

$\frac{5 u^{2} (3 d^{2} c^{3})}{6 d k (d^{2} c^{3})} - \frac{k^{3} y^{3}}{6 c^{3} d^{3}} \cdot \frac{k}{k}$

Step 3.3

Raise

$d$ to the power of

$1$ .

$\frac{5 u^{2} (3 d^{2} c^{3})}{6 (d^{2} d^{1}) k c^{3}} - \frac{k^{3} y^{3}}{6 c^{3} d^{3}} \cdot \frac{k}{k}$

Step 3.4

Use the power rule

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

$\frac{5 u^{2} (3 d^{2} c^{3})}{6 d^{2 + 1} k c^{3}} - \frac{k^{3} y^{3}}{6 c^{3} d^{3}} \cdot \frac{k}{k}$

Step 3.5

Add

$2$ and

$1$ .

$\frac{5 u^{2} (3 d^{2} c^{3})}{6 d^{3} k c^{3}} - \frac{k^{3} y^{3}}{6 c^{3} d^{3}} \cdot \frac{k}{k}$

Step 3.6

Multiply

$\frac{k^{3} y^{3}}{6 c^{3} d^{3}}$ by

$\frac{k}{k}$ .

$\frac{5 u^{2} (3 d^{2} c^{3})}{6 d^{3} k c^{3}} - \frac{k^{3} y^{3} k}{6 c^{3} d^{3} k}$

Step 3.7

Reorder the factors of

$6 d^{3} k c^{3}$ .

$\frac{5 u^{2} (3 d^{2} c^{3})}{6 c^{3} d^{3} k} - \frac{k^{3} y^{3} k}{6 c^{3} d^{3} k}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 u^{2} (3 d^{2} c^{3}) - k^{3} y^{3} k}{6 c^{3} d^{3} k}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

$3$ by

$5$ .

$\frac{15 u^{2} d^{2} c^{3} - k^{3} y^{3} k}{6 c^{3} d^{3} k}$

Step 5.2

Multiply

$k^{3}$ by

$k$ by adding the exponents.

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Step 5.2.1

Move

$k$ .

$\frac{15 u^{2} d^{2} c^{3} - (k \cdot k^{3}) y^{3}}{6 c^{3} d^{3} k}$

Step 5.2.2

Multiply

$k$ by

$k^{3}$ .

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Step 5.2.2.1

Raise

$k$ to the power of

$1$ .

$\frac{15 u^{2} d^{2} c^{3} - (k^{1} k^{3}) y^{3}}{6 c^{3} d^{3} k}$

Step 5.2.2.2

Use the power rule

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

$\frac{15 u^{2} d^{2} c^{3} - k^{1 + 3} y^{3}}{6 c^{3} d^{3} k}$

Step 5.2.3

Add

$1$ and

$3$ .

$\frac{15 u^{2} d^{2} c^{3} - k^{4} y^{3}}{6 c^{3} d^{3} k}$