Algebra Examples

$\frac{y + 8}{2 y - 5} = 1$

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.

$2 y - 5, 1$

Step 1.2

Remove parentheses.

$2 y - 5, 1$

Step 1.3

The LCM of one and any expression is the expression.

$2 y - 5$

Step 2

Multiply each term in $\frac{y + 8}{2 y - 5} = 1$ by $2 y - 5$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{y + 8}{2 y - 5} = 1$ by $2 y - 5$ .

$\frac{y + 8}{2 y - 5} (2 y - 5) = 1 (2 y - 5)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2 y - 5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{y + 8}{2 y - 5} (2 y - 5) = 1 (2 y - 5)$

Step 2.2.1.2

Rewrite the expression.

$y + 8 = 1 (2 y - 5)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $2 y - 5$ by $1$ .

$y + 8 = 2 y - 5$

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 $2 y$ from both sides of the equation.

$y + 8 - 2 y = - 5$

Step 3.1.2

Subtract $2 y$ from $y$ .

$- y + 8 = - 5$

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 $8$ from both sides of the equation.

$- y = - 5 - 8$

Step 3.2.2

Subtract $8$ from $- 5$ .

$- y = - 13$

Step 3.3

Divide each term in $- y = - 13$ by $- 1$ and simplify.

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Step 3.3.1

Divide each term in $- y = - 13$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 13}{- 1}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 13}{- 1}$

Step 3.3.2.2

Divide $y$ by $1$ .

$y = \frac{- 13}{- 1}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 13$ by $- 1$ .

$y = 13$