Pre-Algebra Examples

$\frac{6 x^{5} y + 75 x^{4} y - 24 x^{3} y^{2}}{3 x^{4} y}$

Step 1

Factor $3 x^{3} y$ out of $6 x^{5} y + 75 x^{4} y - 24 x^{3} y^{2}$ .

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Step 1.1

Factor $3 x^{3} y$ out of $6 x^{5} y$ .

$\frac{3 x^{3} y (2 x^{2}) + 75 x^{4} y - 24 x^{3} y^{2}}{3 x^{4} y}$

Step 1.2

Factor $3 x^{3} y$ out of $75 x^{4} y$ .

$\frac{3 x^{3} y (2 x^{2}) + 3 x^{3} y (25 x) - 24 x^{3} y^{2}}{3 x^{4} y}$

Step 1.3

Factor $3 x^{3} y$ out of $- 24 x^{3} y^{2}$ .

$\frac{3 x^{3} y (2 x^{2}) + 3 x^{3} y (25 x) + 3 x^{3} y (- 8 y)}{3 x^{4} y}$

Step 1.4

Factor $3 x^{3} y$ out of $3 x^{3} y (2 x^{2}) + 3 x^{3} y (25 x)$ .

$\frac{3 x^{3} y (2 x^{2} + 25 x) + 3 x^{3} y (- 8 y)}{3 x^{4} y}$

Step 1.5

Factor $3 x^{3} y$ out of $3 x^{3} y (2 x^{2} + 25 x) + 3 x^{3} y (- 8 y)$ .

$\frac{3 x^{3} y (2 x^{2} + 25 x - 8 y)}{3 x^{4} y}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$\frac{3 x^{3} y (2 x^{2} + 25 x - 8 y)}{3 x^{4} y}$

Step 2.2

Rewrite the expression.

$\frac{x^{3} y (2 x^{2} + 25 x - 8 y)}{x^{4} y}$

Step 3

Cancel the common factor of $x^{3}$ and $x^{4}$ .

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Step 3.1

Factor $x^{3}$ out of $x^{3} y (2 x^{2} + 25 x - 8 y)$ .

$\frac{x^{3} (y (2 x^{2} + 25 x - 8 y))}{x^{4} y}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x^{3}$ out of $x^{4} y$ .

$\frac{x^{3} (y (2 x^{2} + 25 x - 8 y))}{x^{3} (x y)}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{3} (y (2 x^{2} + 25 x - 8 y))}{x^{3} (x y)}$

Step 3.2.3

Rewrite the expression.

$\frac{y (2 x^{2} + 25 x - 8 y)}{x y}$

Step 4

Cancel the common factor of $y$ .

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Step 4.1

Cancel the common factor.

$\frac{y (2 x^{2} + 25 x - 8 y)}{x y}$

Step 4.2

Rewrite the expression.

$\frac{2 x^{2} + 25 x - 8 y}{x}$

Step 5

Split the fraction $\frac{2 x^{2} + 25 x - 8 y}{x}$ into two fractions.

$\frac{2 x^{2} + 25 x}{x} + \frac{- 8 y}{x}$

Step 6

Split the fraction $\frac{2 x^{2} + 25 x}{x}$ into two fractions.

$\frac{2 x^{2}}{x} + \frac{25 x}{x} + \frac{- 8 y}{x}$

Step 7

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

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Step 7.1

Factor $x$ out of $2 x^{2}$ .

$\frac{x (2 x)}{x} + \frac{25 x}{x} + \frac{- 8 y}{x}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

$\frac{x (2 x)}{x^{1}} + \frac{25 x}{x} + \frac{- 8 y}{x}$

Step 7.2.2

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

$\frac{x (2 x)}{x \cdot 1} + \frac{25 x}{x} + \frac{- 8 y}{x}$

Step 7.2.3

Cancel the common factor.

$\frac{x (2 x)}{x \cdot 1} + \frac{25 x}{x} + \frac{- 8 y}{x}$

Step 7.2.4

Rewrite the expression.

$\frac{2 x}{1} + \frac{25 x}{x} + \frac{- 8 y}{x}$

Step 7.2.5

Divide $2 x$ by $1$ .

$2 x + \frac{25 x}{x} + \frac{- 8 y}{x}$

Step 8

Cancel the common factor of $x$ .

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Step 8.1

Cancel the common factor.

$2 x + \frac{25 x}{x} + \frac{- 8 y}{x}$

Step 8.2

Divide $25$ by $1$ .

$2 x + 25 + \frac{- 8 y}{x}$

Step 9

Move the negative in front of the fraction.

$2 x + 25 - \frac{8 y}{x}$