Algebra Examples

$\frac{18 x y^{3}}{7 a^{2} b^{2}} \div \frac{12 x^{2} y}{35 a^{2} b}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{18 x y^{3}}{7 a^{2} b^{2}} \cdot \frac{35 a^{2} b}{12 x^{2} y}$

Step 2

Combine.

$\frac{18 x y^{3} (35 a^{2} b)}{7 a^{2} b^{2} (12 x^{2} y)}$

Step 3

Cancel the common factor of $18$ and $12$ .

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Step 3.1

Factor $6$ out of $18 x y^{3} (35 a^{2} b)$ .

$\frac{6 (3 x y^{3} (35 a^{2} b))}{7 a^{2} b^{2} (12 x^{2} y)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $6$ out of $7 a^{2} b^{2} (12 x^{2} y)$ .

$\frac{6 (3 x y^{3} (35 a^{2} b))}{6 (7 a^{2} b^{2} (2 x^{2} y))}$

Step 3.2.2

Cancel the common factor.

$\frac{6 (3 x y^{3} (35 a^{2} b))}{6 (7 a^{2} b^{2} (2 x^{2} y))}$

Step 3.2.3

Rewrite the expression.

$\frac{3 x y^{3} (35 a^{2} b)}{7 a^{2} b^{2} (2 x^{2} y)}$

Step 4

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

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Step 4.1

Factor $x$ out of $3 x y^{3} (35 a^{2} b)$ .

$\frac{x (3 y^{3} (35 a^{2} b))}{7 a^{2} b^{2} (2 x^{2} y)}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $x$ out of $7 a^{2} b^{2} (2 x^{2} y)$ .

$\frac{x (3 y^{3} (35 a^{2} b))}{x (7 a^{2} b^{2} (2 x y))}$

Step 4.2.2

Cancel the common factor.

$\frac{x (3 y^{3} (35 a^{2} b))}{x (7 a^{2} b^{2} (2 x y))}$

Step 4.2.3

Rewrite the expression.

$\frac{3 y^{3} (35 a^{2} b)}{7 a^{2} b^{2} (2 x y)}$

Step 5

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

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Step 5.1

Factor $y$ out of $3 y^{3} (35 a^{2} b)$ .

$\frac{y (3 y^{2} (35 a^{2} b))}{7 a^{2} b^{2} (2 x y)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $y$ out of $7 a^{2} b^{2} (2 x y)$ .

$\frac{y (3 y^{2} (35 a^{2} b))}{y (7 a^{2} b^{2} (2 x))}$

Step 5.2.2

Cancel the common factor.

$\frac{y (3 y^{2} (35 a^{2} b))}{y (7 a^{2} b^{2} (2 x))}$

Step 5.2.3

Rewrite the expression.

$\frac{3 y^{2} (35 a^{2} b)}{7 a^{2} b^{2} (2 x)}$

Step 6

Cancel the common factor of $35$ and $7$ .

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Step 6.1

Factor $7$ out of $3 y^{2} (35 a^{2} b)$ .

$\frac{7 (3 y^{2} (5 a^{2} b))}{7 a^{2} b^{2} (2 x)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $7$ out of $7 a^{2} b^{2} (2 x)$ .

$\frac{7 (3 y^{2} (5 a^{2} b))}{7 (a^{2} b^{2} (2 x))}$

Step 6.2.2

Cancel the common factor.

$\frac{7 (3 y^{2} (5 a^{2} b))}{7 (a^{2} b^{2} (2 x))}$

Step 6.2.3

Rewrite the expression.

$\frac{3 y^{2} (5 a^{2} b)}{a^{2} b^{2} (2 x)}$

Step 7

Cancel the common factor of $a^{2}$ .

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Step 7.1

Cancel the common factor.

$\frac{3 y^{2} (5 a^{2} b)}{a^{2} b^{2} (2 x)}$

Step 7.2

Rewrite the expression.

$\frac{3 y^{2} (5 b)}{b^{2} (2 x)}$

Step 8

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

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Step 8.1

Factor $b$ out of $3 y^{2} (5 b)$ .

$\frac{b (3 y^{2} \cdot (5))}{b^{2} (2 x)}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $b$ out of $b^{2} (2 x)$ .

$\frac{b (3 y^{2} \cdot (5))}{b (b (2 x))}$

Step 8.2.2

Cancel the common factor.

$\frac{b (3 y^{2} \cdot (5))}{b (b (2 x))}$

Step 8.2.3

Rewrite the expression.

$\frac{3 y^{2} \cdot (5)}{b (2 x)}$

Step 9

Simplify the expression.

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Step 9.1

Multiply $5$ by $3$ .

$\frac{15 y^{2}}{b \cdot 2 x}$

Step 9.2

Move $2$ to the left of $b$ .

$\frac{15 y^{2}}{2 b x}$