Algebra Examples

$\frac{5 F + 8}{G} = \frac{3 R - 1}{S}$

Step 1

Multiply both sides by $G$ .

$\frac{5 F + 8}{G} G = \frac{3 R - 1}{S} G$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $G$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{5 F + 8}{G} G = \frac{3 R - 1}{S} G$

Step 2.1.1.2

Rewrite the expression.

$5 F + 8 = \frac{3 R - 1}{S} G$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{3 R - 1}{S} G$ .

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Step 2.2.1.1

Combine $\frac{3 R - 1}{S}$ and $G$ .

$5 F + 8 = \frac{(3 R - 1) G}{S}$

Step 2.2.1.2

Reorder factors in $\frac{(3 R - 1) G}{S}$ .

$5 F + 8 = \frac{G (3 R - 1)}{S}$

Step 3

Solve for $F$ .

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Step 3.1

Subtract $8$ from both sides of the equation.

$5 F = \frac{G (3 R - 1)}{S} - 8$

Step 3.2

Divide each term in $5 F = \frac{G (3 R - 1)}{S} - 8$ by $5$ and simplify.

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Step 3.2.1

Divide each term in $5 F = \frac{G (3 R - 1)}{S} - 8$ by $5$ .

$\frac{5 F}{5} = \frac{\frac{G (3 R - 1)}{S}}{5} + \frac{- 8}{5}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{5 F}{5} = \frac{\frac{G (3 R - 1)}{S}}{5} + \frac{- 8}{5}$

Step 3.2.2.1.2

Divide $F$ by $1$ .

$F = \frac{\frac{G (3 R - 1)}{S}}{5} + \frac{- 8}{5}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Combine the numerators over the common denominator.

$F = \frac{\frac{G (3 R - 1)}{S} - 8}{5}$

Step 3.2.3.2

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{S}{S}$ .

$F = \frac{\frac{G (3 R - 1)}{S} - 8 \cdot \frac{S}{S}}{5}$

Step 3.2.3.3

Simplify terms.

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Step 3.2.3.3.1

Combine $- 8$ and $\frac{S}{S}$ .

$F = \frac{\frac{G (3 R - 1)}{S} + \frac{- 8 S}{S}}{5}$

Step 3.2.3.3.2

Combine the numerators over the common denominator.

$F = \frac{\frac{G (3 R - 1) - 8 S}{S}}{5}$

Step 3.2.3.4

Simplify the numerator.

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Step 3.2.3.4.1

Apply the distributive property.

$F = \frac{\frac{G (3 R) + G \cdot - 1 - 8 S}{S}}{5}$

Step 3.2.3.4.2

Rewrite using the commutative property of multiplication.

$F = \frac{\frac{3 G R + G \cdot - 1 - 8 S}{S}}{5}$

Step 3.2.3.4.3

Move $- 1$ to the left of $G$ .

$F = \frac{\frac{3 G R - 1 \cdot G - 8 S}{S}}{5}$

Step 3.2.3.4.4

Rewrite $- 1 G$ as $- G$ .

$F = \frac{\frac{3 G R - G - 8 S}{S}}{5}$

Step 3.2.3.5

Multiply the numerator by the reciprocal of the denominator.

$F = \frac{3 G R - G - 8 S}{S} \cdot \frac{1}{5}$

Step 3.2.3.6

Multiply $\frac{3 G R - G - 8 S}{S}$ by $\frac{1}{5}$ .

$F = \frac{3 G R - G - 8 S}{S \cdot 5}$

Step 3.2.3.7

Move $5$ to the left of $S$ .

$F = \frac{3 G R - G - 8 S}{5 S}$