Algebra Examples

$\frac{9 r^{3} - 54 r^{2}}{9 r^{2} + 45 r} \cdot \frac{9 r^{2} + 9 r}{9 r^{3} - 54 r^{2}}$

Step 1

Factor $9 r^{2}$ out of $9 r^{3} - 54 r^{2}$ .

Tap for more steps...

Step 1.1

Factor $9 r^{2}$ out of $9 r^{3}$ .

$\frac{9 r^{2} (r) - 54 r^{2}}{9 r^{2} + 45 r} \cdot \frac{9 r^{2} + 9 r}{9 r^{3} - 54 r^{2}}$

Step 1.2

Factor $9 r^{2}$ out of $- 54 r^{2}$ .

$\frac{9 r^{2} (r) + 9 r^{2} (- 6)}{9 r^{2} + 45 r} \cdot \frac{9 r^{2} + 9 r}{9 r^{3} - 54 r^{2}}$

Step 1.3

Factor $9 r^{2}$ out of $9 r^{2} (r) + 9 r^{2} (- 6)$ .

$\frac{9 r^{2} (r - 6)}{9 r^{2} + 45 r} \cdot \frac{9 r^{2} + 9 r}{9 r^{3} - 54 r^{2}}$

Step 2

Factor $9 r$ out of $9 r^{2} + 45 r$ .

Tap for more steps...

Step 2.1

Factor $9 r$ out of $9 r^{2}$ .

$\frac{9 r^{2} (r - 6)}{9 r (r) + 45 r} \cdot \frac{9 r^{2} + 9 r}{9 r^{3} - 54 r^{2}}$

Step 2.2

Factor $9 r$ out of $45 r$ .

$\frac{9 r^{2} (r - 6)}{9 r (r) + 9 r (5)} \cdot \frac{9 r^{2} + 9 r}{9 r^{3} - 54 r^{2}}$

Step 2.3

Factor $9 r$ out of $9 r (r) + 9 r (5)$ .

$\frac{9 r^{2} (r - 6)}{9 r (r + 5)} \cdot \frac{9 r^{2} + 9 r}{9 r^{3} - 54 r^{2}}$

Step 3

Factor $9 r$ out of $9 r^{2} + 9 r$ .

Tap for more steps...

Step 3.1

Factor $9 r$ out of $9 r^{2}$ .

$\frac{9 r^{2} (r - 6)}{9 r (r + 5)} \cdot \frac{9 r (r) + 9 r}{9 r^{3} - 54 r^{2}}$

Step 3.2

Factor $9 r$ out of $9 r$ .

$\frac{9 r^{2} (r - 6)}{9 r (r + 5)} \cdot \frac{9 r (r) + 9 r (1)}{9 r^{3} - 54 r^{2}}$

Step 3.3

Factor $9 r$ out of $9 r (r) + 9 r (1)$ .

$\frac{9 r^{2} (r - 6)}{9 r (r + 5)} \cdot \frac{9 r (r + 1)}{9 r^{3} - 54 r^{2}}$

Step 4

Factor $9 r^{2}$ out of $9 r^{3} - 54 r^{2}$ .

Tap for more steps...

Step 4.1

Factor $9 r^{2}$ out of $9 r^{3}$ .

$\frac{9 r^{2} (r - 6)}{9 r (r + 5)} \cdot \frac{9 r (r + 1)}{9 r^{2} (r) - 54 r^{2}}$

Step 4.2

Factor $9 r^{2}$ out of $- 54 r^{2}$ .

$\frac{9 r^{2} (r - 6)}{9 r (r + 5)} \cdot \frac{9 r (r + 1)}{9 r^{2} (r) + 9 r^{2} (- 6)}$

Step 4.3

Factor $9 r^{2}$ out of $9 r^{2} (r) + 9 r^{2} (- 6)$ .

$\frac{9 r^{2} (r - 6)}{9 r (r + 5)} \cdot \frac{9 r (r + 1)}{9 r^{2} (r - 6)}$

Step 5

Combine.

$\frac{9 r^{2} (r - 6) (9 r (r + 1))}{9 r (r + 5) (9 r^{2} (r - 6))}$

Step 6

Multiply $r^{2}$ by $r$ by adding the exponents.

Tap for more steps...

Step 6.1

Move $r$ .

$\frac{9 (r \cdot r^{2}) (r - 6) (9 (r + 1))}{9 r (r + 5) (9 r^{2} (r - 6))}$

Step 6.2

Multiply $r$ by $r^{2}$ .

Tap for more steps...

Step 6.2.1

Raise $r$ to the power of $1$ .

$\frac{9 (r^{1} r^{2}) (r - 6) (9 (r + 1))}{9 r (r + 5) (9 r^{2} (r - 6))}$

Step 6.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{9 r^{1 + 2} (r - 6) (9 (r + 1))}{9 r (r + 5) (9 r^{2} (r - 6))}$

Step 6.3

Add $1$ and $2$ .

$\frac{9 r^{3} (r - 6) (9 (r + 1))}{9 r (r + 5) (9 r^{2} (r - 6))}$

Step 7

Multiply $r$ by $r^{2}$ by adding the exponents.

Tap for more steps...

Step 7.1

Move $r^{2}$ .

$\frac{9 r^{3} (r - 6) (9 (r + 1))}{9 (r^{2} r) (r + 5) (9 (r - 6))}$

Step 7.2

Multiply $r^{2}$ by $r$ .

Tap for more steps...

Step 7.2.1

Raise $r$ to the power of $1$ .

$\frac{9 r^{3} (r - 6) (9 (r + 1))}{9 (r^{2} r^{1}) (r + 5) (9 (r - 6))}$

Step 7.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{9 r^{3} (r - 6) (9 (r + 1))}{9 r^{2 + 1} (r + 5) (9 (r - 6))}$

Step 7.3

Add $2$ and $1$ .

$\frac{9 r^{3} (r - 6) (9 (r + 1))}{9 r^{3} (r + 5) (9 (r - 6))}$

Step 8

Cancel the common factor of $9$ .

Tap for more steps...

Step 8.1

Cancel the common factor.

$\frac{9 r^{3} (r - 6) (9 (r + 1))}{9 r^{3} (r + 5) (9 (r - 6))}$

Step 8.2

Rewrite the expression.

$\frac{(r^{3} (r - 6)) (9 (r + 1))}{(r^{3} (r + 5)) (9 (r - 6))}$

Step 9

Cancel the common factor of $r^{3}$ .

Tap for more steps...

Step 9.1

Cancel the common factor.

$\frac{r^{3} (r - 6) (9 (r + 1))}{r^{3} (r + 5) (9 (r - 6))}$

Step 9.2

Rewrite the expression.

$\frac{(r - 6) (9 (r + 1))}{(r + 5) (9 (r - 6))}$

Step 10

Cancel the common factor of $r - 6$ .

Tap for more steps...

Step 10.1

Cancel the common factor.

$\frac{(r - 6) (9 (r + 1))}{(r + 5) (9 (r - 6))}$

Step 10.2

Rewrite the expression.

$\frac{9 (r + 1)}{(r + 5) \cdot (9)}$

Step 11

Cancel the common factor of $9$ .

Tap for more steps...

Step 11.1

Cancel the common factor.

$\frac{9 (r + 1)}{(r + 5) \cdot 9}$

Step 11.2

Rewrite the expression.

$\frac{r + 1}{r + 5}$