Algebra Examples

$\frac{5}{4 m^{2}} - \frac{4 m}{2 n}$

Step 1

Cancel the common factor of $4$ and $2$ .

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Step 1.1

Factor $2$ out of $4 m$ .

$\frac{5}{4 m^{2}} - \frac{2 (2 m)}{2 n}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $2 n$ .

$\frac{5}{4 m^{2}} - \frac{2 (2 m)}{2 (n)}$

Step 1.2.2

Cancel the common factor.

$\frac{5}{4 m^{2}} - \frac{2 (2 m)}{2 n}$

Step 1.2.3

Rewrite the expression.

$\frac{5}{4 m^{2}} - \frac{2 m}{n}$

Step 2

To write $\frac{5}{4 m^{2}}$ as a fraction with a common denominator, multiply by $\frac{n}{n}$ .

$\frac{5}{4 m^{2}} \cdot \frac{n}{n} - \frac{2 m}{n}$

Step 3

To write $- \frac{2 m}{n}$ as a fraction with a common denominator, multiply by $\frac{4 m^{2}}{4 m^{2}}$ .

$\frac{5}{4 m^{2}} \cdot \frac{n}{n} - \frac{2 m}{n} \cdot \frac{4 m^{2}}{4 m^{2}}$

Step 4

Write each expression with a common denominator of $4 n m^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{4 m^{2}}$ by $\frac{n}{n}$ .

$\frac{5 n}{4 m^{2} n} - \frac{2 m}{n} \cdot \frac{4 m^{2}}{4 m^{2}}$

Step 4.2

Multiply $\frac{2 m}{n}$ by $\frac{4 m^{2}}{4 m^{2}}$ .

$\frac{5 n}{4 m^{2} n} - \frac{2 m (4 m^{2})}{n (4 m^{2})}$

Step 4.3

Reorder the factors of $n (4 m^{2})$ .

$\frac{5 n}{4 m^{2} n} - \frac{2 m (4 m^{2})}{4 m^{2} n}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 n - 2 m (4 m^{2})}{4 m^{2} n}$

Step 6

Simplify the numerator.

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Step 6.1

Rewrite using the commutative property of multiplication.

$\frac{5 n - 2 \cdot 4 m \cdot m^{2}}{4 m^{2} n}$

Step 6.2

Multiply $m$ by $m^{2}$ by adding the exponents.

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Step 6.2.1

Move $m^{2}$ .

$\frac{5 n - 2 \cdot 4 (m^{2} m)}{4 m^{2} n}$

Step 6.2.2

Multiply $m^{2}$ by $m$ .

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Step 6.2.2.1

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

$\frac{5 n - 2 \cdot 4 (m^{2} m^{1})}{4 m^{2} n}$

Step 6.2.2.2

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

$\frac{5 n - 2 \cdot 4 m^{2 + 1}}{4 m^{2} n}$

Step 6.2.3

Add $2$ and $1$ .

$\frac{5 n - 2 \cdot 4 m^{3}}{4 m^{2} n}$

Step 6.3

Multiply $- 2$ by $4$ .

$\frac{5 n - 8 m^{3}}{4 m^{2} n}$