Pre-Algebra Examples

$\frac{9 x^{2} y^{2} + 15}{- 3 x y}$

Step 1

Cancel the common factor of $9 x^{2} y^{2} + 15$ and $- 3$ .

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Step 1.1

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

$\frac{3 (3 x^{2} y^{2}) + 15}{- 3 x y}$

Step 1.2

Factor $3$ out of $15$ .

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

Step 1.3

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

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

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $3$ out of $- 3 x y$ .

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

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

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

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

Step 2

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $x$ out of $x y$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

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

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Step 5.1

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

$- (\frac{y (3 x y)}{y} + \frac{5}{x y})$

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

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

$- (\frac{y (3 x y)}{y \cdot 1} + \frac{5}{x y})$

Step 5.2.3

Cancel the common factor.

$- (\frac{y (3 x y)}{y \cdot 1} + \frac{5}{x y})$

Step 5.2.4

Rewrite the expression.

$- (\frac{3 x y}{1} + \frac{5}{x y})$

Step 5.2.5

Divide $3 x y$ by $1$ .

$- (3 x y + \frac{5}{x y})$

$- (3 x y + \frac{5}{x y})$

$- (3 x y + \frac{5}{x y})$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$