Algebra Examples

$\frac{27 x^{12} y^{2} + 45 x^{9} z^{5}}{9 x^{3} y^{3} z^{7}}$

Step 1

Factor $9 x^{9}$ out of $27 x^{12} y^{2} + 45 x^{9} z^{5}$ .

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Step 1.1

Factor $9 x^{9}$ out of $27 x^{12} y^{2}$ .

$\frac{9 x^{9} (3 x^{3} y^{2}) + 45 x^{9} z^{5}}{9 x^{3} y^{3} z^{7}}$

Step 1.2

Factor $9 x^{9}$ out of $45 x^{9} z^{5}$ .

$\frac{9 x^{9} (3 x^{3} y^{2}) + 9 x^{9} (5 z^{5})}{9 x^{3} y^{3} z^{7}}$

Step 1.3

Factor $9 x^{9}$ out of $9 x^{9} (3 x^{3} y^{2}) + 9 x^{9} (5 z^{5})$ .

$\frac{9 x^{9} (3 x^{3} y^{2} + 5 z^{5})}{9 x^{3} y^{3} z^{7}}$

Step 2

Cancel the common factor of $9$ .

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Step 2.1

Cancel the common factor.

$\frac{9 x^{9} (3 x^{3} y^{2} + 5 z^{5})}{9 x^{3} y^{3} z^{7}}$

Step 2.2

Rewrite the expression.

$\frac{x^{9} (3 x^{3} y^{2} + 5 z^{5})}{x^{3} y^{3} z^{7}}$

Step 3

Cancel the common factor of $x^{9}$ and $x^{3}$ .

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Step 3.1

Factor $x^{3}$ out of $x^{9} (3 x^{3} y^{2} + 5 z^{5})$ .

$\frac{x^{3} (x^{6} (3 x^{3} y^{2} + 5 z^{5}))}{x^{3} y^{3} z^{7}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x^{3}$ out of $x^{3} y^{3} z^{7}$ .

$\frac{x^{3} (x^{6} (3 x^{3} y^{2} + 5 z^{5}))}{x^{3} (y^{3} z^{7})}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{3} (x^{6} (3 x^{3} y^{2} + 5 z^{5}))}{x^{3} (y^{3} z^{7})}$

Step 3.2.3

Rewrite the expression.

$\frac{x^{6} (3 x^{3} y^{2} + 5 z^{5})}{y^{3} z^{7}}$

Step 4

Apply the distributive property.

$\frac{x^{6} (3 x^{3} y^{2}) + x^{6} (5 z^{5})}{y^{3} z^{7}}$

Step 5

Rewrite using the commutative property of multiplication.

$\frac{3 x^{6} (x^{3} y^{2}) + x^{6} (5 z^{5})}{y^{3} z^{7}}$

Step 6

Rewrite using the commutative property of multiplication.

$\frac{3 x^{6} (x^{3} y^{2}) + 5 x^{6} z^{5}}{y^{3} z^{7}}$

Step 7

Multiply $x^{6}$ by $x^{3}$ by adding the exponents.

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Step 7.1

Move $x^{3}$ .

$\frac{3 (x^{3} x^{6}) y^{2} + 5 x^{6} z^{5}}{y^{3} z^{7}}$

Step 7.2

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

$\frac{3 x^{3 + 6} y^{2} + 5 x^{6} z^{5}}{y^{3} z^{7}}$

Step 7.3

Add $3$ and $6$ .

$\frac{3 x^{9} y^{2} + 5 x^{6} z^{5}}{y^{3} z^{7}}$

Step 8

Split the fraction $\frac{3 x^{9} y^{2} + 5 x^{6} z^{5}}{y^{3} z^{7}}$ into two fractions.

$\frac{3 x^{9} y^{2}}{y^{3} z^{7}} + \frac{5 x^{6} z^{5}}{y^{3} z^{7}}$

Step 9

Cancel the common factor of $y^{2}$ and $y^{3}$ .

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Step 9.1

Factor $y^{2}$ out of $3 x^{9} y^{2}$ .

$\frac{y^{2} (3 x^{9})}{y^{3} z^{7}} + \frac{5 x^{6} z^{5}}{y^{3} z^{7}}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $y^{2}$ out of $y^{3} z^{7}$ .

$\frac{y^{2} (3 x^{9})}{y^{2} (y z^{7})} + \frac{5 x^{6} z^{5}}{y^{3} z^{7}}$

Step 9.2.2

Cancel the common factor.

$\frac{y^{2} (3 x^{9})}{y^{2} (y z^{7})} + \frac{5 x^{6} z^{5}}{y^{3} z^{7}}$

Step 9.2.3

Rewrite the expression.

$\frac{3 x^{9}}{y z^{7}} + \frac{5 x^{6} z^{5}}{y^{3} z^{7}}$

Step 10

Cancel the common factor of $z^{5}$ and $z^{7}$ .

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Step 10.1

Factor $z^{5}$ out of $5 x^{6} z^{5}$ .

$\frac{3 x^{9}}{y z^{7}} + \frac{z^{5} (5 x^{6})}{y^{3} z^{7}}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $z^{5}$ out of $y^{3} z^{7}$ .

$\frac{3 x^{9}}{y z^{7}} + \frac{z^{5} (5 x^{6})}{z^{5} (y^{3} z^{2})}$

Step 10.2.2

Cancel the common factor.

$\frac{3 x^{9}}{y z^{7}} + \frac{z^{5} (5 x^{6})}{z^{5} (y^{3} z^{2})}$

Step 10.2.3

Rewrite the expression.

$\frac{3 x^{9}}{y z^{7}} + \frac{5 x^{6}}{y^{3} z^{2}}$