Finite Math Examples

$\frac{g}{f} \cdot (- 3) = \frac{5 - 2 {(- 3)}^{2}}{6 - 2 \cdot - 3}$

Step 1

Simplify $\frac{g}{f} \cdot - 3$ .

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Step 1.1

Combine $\frac{g}{f}$ and $- 3$ .

$\frac{g \cdot - 3}{f} = \frac{5 - 2 {(- 3)}^{2}}{6 - 2 \cdot - 3}$

Step 1.2

Simplify the expression.

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Step 1.2.1

Move $- 3$ to the left of $g$ .

$\frac{- 3 \cdot g}{f} = \frac{5 - 2 {(- 3)}^{2}}{6 - 2 \cdot - 3}$

Step 1.2.2

Move the negative in front of the fraction.

$- \frac{3 g}{f} = \frac{5 - 2 {(- 3)}^{2}}{6 - 2 \cdot - 3}$

Step 2

Simplify $\frac{5 - 2 {(- 3)}^{2}}{6 - 2 \cdot - 3}$ .

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Raise $- 3$ to the power of $2$ .

$- \frac{3 g}{f} = \frac{5 - 2 \cdot 9}{6 - 2 \cdot - 3}$

Step 2.1.2

Multiply $- 2$ by $9$ .

$- \frac{3 g}{f} = \frac{5 - 18}{6 - 2 \cdot - 3}$

Step 2.1.3

Subtract $18$ from $5$ .

$- \frac{3 g}{f} = \frac{- 13}{6 - 2 \cdot - 3}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Multiply $- 2$ by $- 3$ .

$- \frac{3 g}{f} = \frac{- 13}{6 + 6}$

Step 2.2.2

Add $6$ and $6$ .

$- \frac{3 g}{f} = \frac{- 13}{12}$

Step 2.3

Move the negative in front of the fraction.

$- \frac{3 g}{f} = - \frac{13}{12}$

Step 3

Divide each term in $- \frac{3 g}{f} = - \frac{13}{12}$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- \frac{3 g}{f} = - \frac{13}{12}$ by $- 1$ .

$\frac{- \frac{3 g}{f}}{- 1} = \frac{- \frac{13}{12}}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{3 g}{f}}{1} = \frac{- \frac{13}{12}}{- 1}$

Step 3.2.2

Divide $\frac{3 g}{f}$ by $1$ .

$\frac{3 g}{f} = \frac{- \frac{13}{12}}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

$\frac{3 g}{f} = \frac{\frac{13}{12}}{1}$

Step 3.3.2

Divide $\frac{13}{12}$ by $1$ .

$\frac{3 g}{f} = \frac{13}{12}$

Step 4

Multiply both sides by $f$ .

$\frac{3 g}{f} f = \frac{13}{12} f$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $f$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{3 g}{f} f = \frac{13}{12} f$

Step 5.1.1.2

Rewrite the expression.

$3 g = \frac{13}{12} f$

Step 5.2

Simplify the right side.

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Step 5.2.1

Combine $\frac{13}{12}$ and $f$ .

$3 g = \frac{13 f}{12}$

Step 6

Divide each term in $3 g = \frac{13 f}{12}$ by $3$ and simplify.

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Step 6.1

Divide each term in $3 g = \frac{13 f}{12}$ by $3$ .

$\frac{3 g}{3} = \frac{\frac{13 f}{12}}{3}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $3$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{3 g}{3} = \frac{\frac{13 f}{12}}{3}$

Step 6.2.1.2

Divide $g$ by $1$ .

$g = \frac{\frac{13 f}{12}}{3}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Multiply the numerator by the reciprocal of the denominator.

$g = \frac{13 f}{12} \cdot \frac{1}{3}$

Step 6.3.2

Multiply $\frac{13 f}{12} \cdot \frac{1}{3}$ .

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Step 6.3.2.1

Multiply $\frac{13 f}{12}$ by $\frac{1}{3}$ .

$g = \frac{13 f}{12 \cdot 3}$

Step 6.3.2.2

Multiply $12$ by $3$ .

$g = \frac{13 f}{36}$