Algebra Examples

$\frac{y + 4}{3 y - 8} = 1$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$3 y - 8, 1$

Step 1.2

Remove parentheses.

$3 y - 8, 1$

Step 1.3

The LCM of one and any expression is the expression.

$3 y - 8$

Step 2

Multiply each term in $\frac{y + 4}{3 y - 8} = 1$ by $3 y - 8$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{y + 4}{3 y - 8} = 1$ by $3 y - 8$ .

$\frac{y + 4}{3 y - 8} (3 y - 8) = 1 (3 y - 8)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3 y - 8$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{y + 4}{3 y - 8} (3 y - 8) = 1 (3 y - 8)$

Step 2.2.1.2

Rewrite the expression.

$y + 4 = 1 (3 y - 8)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $3 y - 8$ by $1$ .

$y + 4 = 3 y - 8$

Step 3

Solve the equation.

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Step 3.1

Move all terms containing $y$ to the left side of the equation.

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Step 3.1.1

Subtract $3 y$ from both sides of the equation.

$y + 4 - 3 y = - 8$

Step 3.1.2

Subtract $3 y$ from $y$ .

$- 2 y + 4 = - 8$

Step 3.2

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

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Step 3.2.1

Subtract $4$ from both sides of the equation.

$- 2 y = - 8 - 4$

Step 3.2.2

Subtract $4$ from $- 8$ .

$- 2 y = - 12$

Step 3.3

Divide each term in $- 2 y = - 12$ by $- 2$ and simplify.

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Step 3.3.1

Divide each term in $- 2 y = - 12$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 12}{- 2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 12}{- 2}$

Step 3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 12}{- 2}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 12$ by $- 2$ .

$y = 6$