Calculus Examples

$\frac{16}{m^{2}} + \frac{m - 4}{m - 3}$

Step 1

To write $\frac{16}{m^{2}}$ as a fraction with a common denominator, multiply by $\frac{m - 3}{m - 3}$ .

$\frac{16}{m^{2}} \cdot \frac{m - 3}{m - 3} + \frac{m - 4}{m - 3}$

Step 2

To write $\frac{m - 4}{m - 3}$ as a fraction with a common denominator, multiply by $\frac{m^{2}}{m^{2}}$ .

$\frac{16}{m^{2}} \cdot \frac{m - 3}{m - 3} + \frac{m - 4}{m - 3} \cdot \frac{m^{2}}{m^{2}}$

Step 3

Write each expression with a common denominator of $(m - 3) m^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{16}{m^{2}}$ by $\frac{m - 3}{m - 3}$ .

$\frac{16 (m - 3)}{m^{2} (m - 3)} + \frac{m - 4}{m - 3} \cdot \frac{m^{2}}{m^{2}}$

Step 3.2

Multiply $\frac{m - 4}{m - 3}$ by $\frac{m^{2}}{m^{2}}$ .

$\frac{16 (m - 3)}{m^{2} (m - 3)} + \frac{(m - 4) m^{2}}{(m - 3) m^{2}}$

Step 3.3

Reorder the factors of $(m - 3) m^{2}$ .

$\frac{16 (m - 3)}{m^{2} (m - 3)} + \frac{(m - 4) m^{2}}{m^{2} (m - 3)}$

Step 4

Combine the numerators over the common denominator.

$\frac{16 (m - 3) + (m - 4) m^{2}}{m^{2} (m - 3)}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{16 m + 16 \cdot - 3 + (m - 4) m^{2}}{m^{2} (m - 3)}$

Step 5.2

Multiply $16$ by $- 3$ .

$\frac{16 m - 48 + (m - 4) m^{2}}{m^{2} (m - 3)}$

Step 5.3

Apply the distributive property.

$\frac{16 m - 48 + m \cdot m^{2} - 4 m^{2}}{m^{2} (m - 3)}$

Step 5.4

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

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Step 5.4.1

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

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Step 5.4.1.1

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

$\frac{16 m - 48 + m^{1} m^{2} - 4 m^{2}}{m^{2} (m - 3)}$

Step 5.4.1.2

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

$\frac{16 m - 48 + m^{1 + 2} - 4 m^{2}}{m^{2} (m - 3)}$

Step 5.4.2

Add $1$ and $2$ .

$\frac{16 m - 48 + m^{3} - 4 m^{2}}{m^{2} (m - 3)}$

Step 5.5

Reorder terms.

$\frac{m^{3} - 4 m^{2} + 16 m - 48}{m^{2} (m - 3)}$