Algebra Examples

$\frac{9 z + 36}{z + 4} = \frac{6}{z - 9} + 3$

Step 1

Factor each term.

Tap for more steps...

Step 1.1

Factor $9$ out of $9 z + 36$ .

Tap for more steps...

Step 1.1.1

Factor $9$ out of $9 z$ .

$\frac{9 (z) + 36}{z + 4} = \frac{6}{z - 9} + 3$

Step 1.1.2

Factor $9$ out of $36$ .

$\frac{9 z + 9 \cdot 4}{z + 4} = \frac{6}{z - 9} + 3$

Step 1.1.3

Factor $9$ out of $9 z + 9 \cdot 4$ .

$\frac{9 (z + 4)}{z + 4} = \frac{6}{z - 9} + 3$

Step 1.2

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 1.2.1

Reduce the expression $\frac{9 (z + 4)}{z + 4}$ by cancelling the common factors.

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{9 (z + 4)}{z + 4} = \frac{6}{z - 9} + 3$

Step 1.2.1.2

Rewrite the expression.

$\frac{9}{1} = \frac{6}{z - 9} + 3$

Step 1.2.2

Divide $9$ by $1$ .

$9 = \frac{6}{z - 9} + 3$

Step 2

Find the LCD of the terms in the equation.

Tap for more steps...

Step 2.1

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

$1, z - 9, 1$

Step 2.2

Remove parentheses.

$1, z - 9, 1$

Step 2.3

The LCM of one and any expression is the expression.

$z - 9$

Step 3

Multiply each term in $9 = \frac{6}{z - 9} + 3$ by $z - 9$ to eliminate the fractions.

Tap for more steps...

Step 3.1

Multiply each term in $9 = \frac{6}{z - 9} + 3$ by $z - 9$ .

$9 (z - 9) = \frac{6}{z - 9} (z - 9) + 3 (z - 9)$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Apply the distributive property.

$9 z + 9 \cdot - 9 = \frac{6}{z - 9} (z - 9) + 3 (z - 9)$

Step 3.2.2

Multiply $9$ by $- 9$ .

$9 z - 81 = \frac{6}{z - 9} (z - 9) + 3 (z - 9)$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Simplify each term.

Tap for more steps...

Step 3.3.1.1

Cancel the common factor of $z - 9$ .

Tap for more steps...

Step 3.3.1.1.1

Cancel the common factor.

$9 z - 81 = \frac{6}{z - 9} (z - 9) + 3 (z - 9)$

Step 3.3.1.1.2

Rewrite the expression.

$9 z - 81 = 6 + 3 (z - 9)$

Step 3.3.1.2

Apply the distributive property.

$9 z - 81 = 6 + 3 z + 3 \cdot - 9$

Step 3.3.1.3

Multiply $3$ by $- 9$ .

$9 z - 81 = 6 + 3 z - 27$

Step 3.3.2

Subtract $27$ from $6$ .

$9 z - 81 = 3 z - 21$

Step 4

Solve the equation.

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

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

$9 z - 81 - 3 z = - 21$

Step 4.1.2

Subtract $3 z$ from $9 z$ .

$6 z - 81 = - 21$

Step 4.2

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

Tap for more steps...

Step 4.2.1

Add $81$ to both sides of the equation.

$6 z = - 21 + 81$

Step 4.2.2

Add $- 21$ and $81$ .

$6 z = 60$

Step 4.3

Divide each term in $6 z = 60$ by $6$ and simplify.

Tap for more steps...

Step 4.3.1

Divide each term in $6 z = 60$ by $6$ .

$\frac{6 z}{6} = \frac{60}{6}$

Step 4.3.2

Simplify the left side.

Tap for more steps...

Step 4.3.2.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 4.3.2.1.1

Cancel the common factor.

$\frac{6 z}{6} = \frac{60}{6}$

Step 4.3.2.1.2

Divide $z$ by $1$ .

$z = \frac{60}{6}$

Step 4.3.3

Simplify the right side.

Tap for more steps...

Step 4.3.3.1

Divide $60$ by $6$ .

$z = 10$