Precalculus Examples

$\frac{9 m - 1}{8 m + 2} - \frac{5}{7 m^{2}}$

Step 1

Factor $2$ out of $8 m + 2$ .

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Step 1.1

Factor $2$ out of $8 m$ .

$\frac{9 m - 1}{2 (4 m) + 2} - \frac{5}{7 m^{2}}$

Step 1.2

Factor $2$ out of $2$ .

$\frac{9 m - 1}{2 (4 m) + 2 (1)} - \frac{5}{7 m^{2}}$

Step 1.3

Factor $2$ out of $2 (4 m) + 2 (1)$ .

$\frac{9 m - 1}{2 (4 m + 1)} - \frac{5}{7 m^{2}}$

Step 2

To write $\frac{9 m - 1}{2 (4 m + 1)}$ as a fraction with a common denominator, multiply by $\frac{7 m^{2}}{7 m^{2}}$ .

$\frac{9 m - 1}{2 (4 m + 1)} \cdot \frac{7 m^{2}}{7 m^{2}} - \frac{5}{7 m^{2}}$

Step 3

To write $- \frac{5}{7 m^{2}}$ as a fraction with a common denominator, multiply by $\frac{2 (4 m + 1)}{2 (4 m + 1)}$ .

$\frac{9 m - 1}{2 (4 m + 1)} \cdot \frac{7 m^{2}}{7 m^{2}} - \frac{5}{7 m^{2}} \cdot \frac{2 (4 m + 1)}{2 (4 m + 1)}$

Step 4

Write each expression with a common denominator of $14 (4 m + 1) m^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{9 m - 1}{2 (4 m + 1)}$ by $\frac{7 m^{2}}{7 m^{2}}$ .

$\frac{(9 m - 1) (7 m^{2})}{2 (4 m + 1) (7 m^{2})} - \frac{5}{7 m^{2}} \cdot \frac{2 (4 m + 1)}{2 (4 m + 1)}$

Step 4.2

Multiply $7$ by $2$ .

$\frac{(9 m - 1) (7 m^{2})}{14 (4 m + 1) m^{2}} - \frac{5}{7 m^{2}} \cdot \frac{2 (4 m + 1)}{2 (4 m + 1)}$

Step 4.3

Multiply $\frac{5}{7 m^{2}}$ by $\frac{2 (4 m + 1)}{2 (4 m + 1)}$ .

$\frac{(9 m - 1) (7 m^{2})}{14 (4 m + 1) m^{2}} - \frac{5 (2 (4 m + 1))}{7 m^{2} (2 (4 m + 1))}$

Step 4.4

Multiply $2$ by $7$ .

$\frac{(9 m - 1) (7 m^{2})}{14 (4 m + 1) m^{2}} - \frac{5 (2 (4 m + 1))}{14 m^{2} (4 m + 1)}$

Step 4.5

Reorder the factors of $14 (4 m + 1) m^{2}$ .

$\frac{(9 m - 1) (7 m^{2})}{14 m^{2} (4 m + 1)} - \frac{5 (2 (4 m + 1))}{14 m^{2} (4 m + 1)}$

Step 5

Combine the numerators over the common denominator.

$\frac{(9 m - 1) (7 m^{2}) - 5 (2 (4 m + 1))}{14 m^{2} (4 m + 1)}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$\frac{(9 m \cdot 7 - 1 \cdot 7) m^{2} - 5 \cdot 2 (4 m + 1)}{14 m^{2} (4 m + 1)}$

Step 6.2

Multiply $7$ by $9$ .

$\frac{(63 m - 1 \cdot 7) m^{2} - 5 \cdot 2 (4 m + 1)}{14 m^{2} (4 m + 1)}$

Step 6.3

Multiply $- 1$ by $7$ .

$\frac{(63 m - 7) m^{2} - 5 \cdot 2 (4 m + 1)}{14 m^{2} (4 m + 1)}$

Step 6.4

Apply the distributive property.

$\frac{63 m \cdot m^{2} - 7 m^{2} - 5 \cdot 2 (4 m + 1)}{14 m^{2} (4 m + 1)}$

Step 6.5

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

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Step 6.5.1

Move $m^{2}$ .

$\frac{63 (m^{2} m) - 7 m^{2} - 5 \cdot 2 (4 m + 1)}{14 m^{2} (4 m + 1)}$

Step 6.5.2

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

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Step 6.5.2.1

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

$\frac{63 (m^{2} m^{1}) - 7 m^{2} - 5 \cdot 2 (4 m + 1)}{14 m^{2} (4 m + 1)}$

Step 6.5.2.2

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

$\frac{63 m^{2 + 1} - 7 m^{2} - 5 \cdot 2 (4 m + 1)}{14 m^{2} (4 m + 1)}$

Step 6.5.3

Add $2$ and $1$ .

$\frac{63 m^{3} - 7 m^{2} - 5 \cdot 2 (4 m + 1)}{14 m^{2} (4 m + 1)}$

Step 6.6

Multiply $- 5$ by $2$ .

$\frac{63 m^{3} - 7 m^{2} - 10 (4 m + 1)}{14 m^{2} (4 m + 1)}$

Step 6.7

Apply the distributive property.

$\frac{63 m^{3} - 7 m^{2} - 10 (4 m) - 10 \cdot 1}{14 m^{2} (4 m + 1)}$

Step 6.8

Multiply $4$ by $- 10$ .

$\frac{63 m^{3} - 7 m^{2} - 40 m - 10 \cdot 1}{14 m^{2} (4 m + 1)}$

Step 6.9

Multiply $- 10$ by $1$ .

$\frac{63 m^{3} - 7 m^{2} - 40 m - 10}{14 m^{2} (4 m + 1)}$