Pre-Algebra Examples

$\frac{x^{2} - 25}{6 x} \div \frac{5 - x}{3 x y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - 25}{6 x} \cdot \frac{3 x y}{5 - x}$

Step 2

Cancel the common factor of $3 x$ .

Tap for more steps...

Step 2.1

Factor $3 x$ out of $6 x$ .

$\frac{x^{2} - 25}{3 x (2)} \cdot \frac{3 x y}{5 - x}$

Step 2.2

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

$\frac{x^{2} - 25}{3 x (2)} \cdot \frac{3 x (y)}{5 - x}$

Step 2.3

Cancel the common factor.

$\frac{x^{2} - 25}{3 x \cdot 2} \cdot \frac{3 x y}{5 - x}$

Step 2.4

Rewrite the expression.

$\frac{x^{2} - 25}{2} \cdot \frac{y}{5 - x}$

Step 3

Multiply $\frac{x^{2} - 25}{2}$ by $\frac{y}{5 - x}$ .

$\frac{(x^{2} - 25) y}{2 (5 - x)}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Rewrite $25$ as $5^{2}$ .

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

Step 4.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 5$ .

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

Step 5

Cancel the common factor of $x - 5$ and $5 - x$ .

Tap for more steps...

Step 5.1

Factor $- 1$ out of $x$ .

$\frac{(x + 5) (- 1 (- x) - 5) y}{2 (5 - x)}$

Step 5.2

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{(x + 5) (- 1 (- x) - 1 (5)) y}{2 (5 - x)}$

Step 5.3

Factor $- 1$ out of $- 1 (- x) - 1 (5)$ .

$\frac{(x + 5) (- 1 (- x + 5)) y}{2 (5 - x)}$

Step 5.4

Reorder terms.

$\frac{(x + 5) (- 1 (- x + 5)) y}{2 (- x + 5)}$

Step 5.5

Cancel the common factor.

$\frac{(x + 5) (- 1 (- x + 5)) y}{2 (- x + 5)}$

Step 5.6

Rewrite the expression.

$\frac{((x + 5) \cdot (- 1)) y}{2}$

Step 6

Factor out negative.

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

Step 7

Move the negative in front of the fraction.

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

Step 8

Reorder factors in $- \frac{(x + 5) y}{2}$ .

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

Step 9

Apply the distributive property.

$- \frac{y x + y \cdot 5}{2}$

Step 10

Move $5$ to the left of $y$ .

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

Step 11

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

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