Solve for h 10/(8+h)=9/3-2

$\frac{10}{8 + h} = \frac{9}{3} - 2$

Step 1

Factor each term.

Divide $9$ by $3$ .

$\frac{10}{8 + h} = 3 - 2$

Subtract $2$ from $3$ .

$\frac{10}{8 + h} = 1$

Step 2

Find the LCD of the terms in the equation.

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

$8 + h, 1$

Remove parentheses.

$8 + h, 1$

The LCM of one and any expression is the expression.

$8 + h$

Step 3

Multiply each term in $\frac{10}{8 + h} = 1$ by $8 + h$ to eliminate the fractions.

Multiply each term in $\frac{10}{8 + h} = 1$ by $8 + h$ .

$\frac{10}{8 + h} (8 + h) = 1 (8 + h)$

Simplify the left side.

Cancel the common factor of $8 + h$ .

Cancel the common factor.

$\frac{10}{8 + h} (8 + h) = 1 (8 + h)$

Rewrite the expression.

$10 = 1 (8 + h)$

Simplify the right side.

Multiply $8 + h$ by $1$ .

$10 = 8 + h$

Step 4

Solve the equation.

Rewrite the equation as $8 + h = 10$ .

$8 + h = 10$

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

Subtract $8$ from both sides of the equation.

$h = 10 - 8$

Subtract $8$ from $10$ .

$h = 2$