Pre-Algebra Examples

$\frac{25 x^{7} y^{4} + 15 x y^{2} + 10 x y^{3}}{5 x y^{3}}$

Step 1

Factor $5 x y^{2}$ out of $25 x^{7} y^{4} + 15 x y^{2} + 10 x y^{3}$ .

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Step 1.1

Factor $5 x y^{2}$ out of $25 x^{7} y^{4}$ .

$\frac{5 x y^{2} (5 x^{6} y^{2}) + 15 x y^{2} + 10 x y^{3}}{5 x y^{3}}$

Step 1.2

Factor $5 x y^{2}$ out of $15 x y^{2}$ .

$\frac{5 x y^{2} (5 x^{6} y^{2}) + 5 x y^{2} (3) + 10 x y^{3}}{5 x y^{3}}$

Step 1.3

Factor $5 x y^{2}$ out of $10 x y^{3}$ .

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

Step 1.4

Factor $5 x y^{2}$ out of $5 x y^{2} (5 x^{6} y^{2}) + 5 x y^{2} (3)$ .

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

Step 1.5

Factor $5 x y^{2}$ out of $5 x y^{2} (5 x^{6} y^{2} + 3) + 5 x y^{2} (2 y)$ .

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

Step 2

Cancel the common factor of $5$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Cancel the common factors.

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Step 4.1

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

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

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

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

Step 6

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

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

Step 7

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

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Step 7.1

Factor $y$ out of $5 x^{6} y^{2}$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

$\frac{y (5 x^{6} y)}{y^{1}} + \frac{3}{y} + \frac{2 y}{y}$

Step 7.2.2

Factor $y$ out of $y^{1}$ .

$\frac{y (5 x^{6} y)}{y \cdot 1} + \frac{3}{y} + \frac{2 y}{y}$

Step 7.2.3

Cancel the common factor.

$\frac{y (5 x^{6} y)}{y \cdot 1} + \frac{3}{y} + \frac{2 y}{y}$

Step 7.2.4

Rewrite the expression.

$\frac{5 x^{6} y}{1} + \frac{3}{y} + \frac{2 y}{y}$

Step 7.2.5

Divide $5 x^{6} y$ by $1$ .

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

Step 8

Cancel the common factor of $y$ .

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Step 8.1

Cancel the common factor.

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

Step 8.2

Divide $2$ by $1$ .

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