Algebra Examples

$\frac{y - 1}{x + 3} = - \frac{3}{4}$

Step 1

Multiply both sides by $x + 3$ .

$\frac{y - 1}{x + 3} (x + 3) = - \frac{3}{4} (x + 3)$

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 $x + 3$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{y - 1}{x + 3} (x + 3) = - \frac{3}{4} (x + 3)$

Step 2.1.1.2

Rewrite the expression.

$y - 1 = - \frac{3}{4} (x + 3)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- \frac{3}{4} (x + 3)$ .

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Step 2.2.1.1

Apply the distributive property.

$y - 1 = - \frac{3}{4} x - \frac{3}{4} \cdot 3$

Step 2.2.1.2

Combine $x$ and $\frac{3}{4}$ .

$y - 1 = - \frac{x \cdot 3}{4} - \frac{3}{4} \cdot 3$

Step 2.2.1.3

Multiply $- \frac{3}{4} \cdot 3$ .

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Step 2.2.1.3.1

Multiply $3$ by $- 1$ .

$y - 1 = - \frac{x \cdot 3}{4} - 3 (\frac{3}{4})$

Step 2.2.1.3.2

Combine $- 3$ and $\frac{3}{4}$ .

$y - 1 = - \frac{x \cdot 3}{4} + \frac{- 3 \cdot 3}{4}$

Step 2.2.1.3.3

Multiply $- 3$ by $3$ .

$y - 1 = - \frac{x \cdot 3}{4} + \frac{- 9}{4}$

Step 2.2.1.4

Simplify each term.

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Step 2.2.1.4.1

Move $3$ to the left of $x$ .

$y - 1 = - \frac{3 \cdot x}{4} + \frac{- 9}{4}$

Step 2.2.1.4.2

Move the negative in front of the fraction.

$y - 1 = - \frac{3 x}{4} - \frac{9}{4}$

Step 3

Move all terms not containing $y$ to the right side of the equation.

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Step 3.1

Add $1$ to both sides of the equation.

$y = - \frac{3 x}{4} - \frac{9}{4} + 1$

Step 3.2

Write $1$ as a fraction with a common denominator.

$y = - \frac{3 x}{4} - \frac{9}{4} + \frac{4}{4}$

Step 3.3

Combine the numerators over the common denominator.

$y = - \frac{3 x}{4} + \frac{- 9 + 4}{4}$

Step 3.4

Add $- 9$ and $4$ .

$y = - \frac{3 x}{4} + \frac{- 5}{4}$

Step 3.5

Move the negative in front of the fraction.

$y = - \frac{3 x}{4} - \frac{5}{4}$