Algebra Examples

$\frac{\frac{1}{2} - \frac{x + 5}{4}}{\frac{x^{2}}{2} - \frac{5}{2}}$

Step 1

Multiply the numerator and denominator of the fraction by $4$ .

Tap for more steps...

Step 1.1

Multiply $\frac{\frac{1}{2} - \frac{x + 5}{4}}{\frac{x^{2}}{2} - \frac{5}{2}}$ by $\frac{4}{4}$ .

$\frac{4}{4} \cdot \frac{\frac{1}{2} - \frac{x + 5}{4}}{\frac{x^{2}}{2} - \frac{5}{2}}$

Step 1.2

Combine.

$\frac{4 (\frac{1}{2} - \frac{x + 5}{4})}{4 (\frac{x^{2}}{2} - \frac{5}{2})}$

Step 2

Apply the distributive property.

$\frac{4 (\frac{1}{2}) + 4 (- \frac{x + 5}{4})}{4 \frac{x^{2}}{2} + 4 (- \frac{5}{2})}$

Step 3

Simplify by cancelling.

Tap for more steps...

Step 3.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.1

Factor $2$ out of $4$ .

$\frac{2 (2) \frac{1}{2} + 4 (- \frac{x + 5}{4})}{4 \frac{x^{2}}{2} + 4 (- \frac{5}{2})}$

Step 3.1.2

Cancel the common factor.

$\frac{2 \cdot 2 \frac{1}{2} + 4 (- \frac{x + 5}{4})}{4 \frac{x^{2}}{2} + 4 (- \frac{5}{2})}$

Step 3.1.3

Rewrite the expression.

$\frac{2 + 4 (- \frac{x + 5}{4})}{4 \frac{x^{2}}{2} + 4 (- \frac{5}{2})}$

Step 3.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.2.1

Move the leading negative in $- \frac{x + 5}{4}$ into the numerator.

$\frac{2 + 4 \frac{- (x + 5)}{4}}{4 \frac{x^{2}}{2} + 4 (- \frac{5}{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{2 + 4 \frac{- (x + 5)}{4}}{4 \frac{x^{2}}{2} + 4 (- \frac{5}{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{2 - (x + 5)}{4 \frac{x^{2}}{2} + 4 (- \frac{5}{2})}$

Step 3.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.3.1

Factor $2$ out of $4$ .

$\frac{2 - (x + 5)}{2 (2) \frac{x^{2}}{2} + 4 (- \frac{5}{2})}$

Step 3.3.2

Cancel the common factor.

$\frac{2 - (x + 5)}{2 \cdot 2 \frac{x^{2}}{2} + 4 (- \frac{5}{2})}$

Step 3.3.3

Rewrite the expression.

$\frac{2 - (x + 5)}{2 x^{2} + 4 (- \frac{5}{2})}$

Step 3.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.4.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{2 - (x + 5)}{2 x^{2} + 4 (\frac{- 5}{2})}$

Step 3.4.2

Factor $2$ out of $4$ .

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

Step 3.4.3

Cancel the common factor.

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

Step 3.4.4

Rewrite the expression.

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

Step 3.5

Multiply $2$ by $- 5$ .

$\frac{2 - (x + 5)}{2 x^{2} - 10}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Apply the distributive property.

$\frac{2 - x - 1 \cdot 5}{2 x^{2} - 10}$

Step 4.2

Multiply $- 1$ by $5$ .

$\frac{2 - x - 5}{2 x^{2} - 10}$

Step 4.3

Subtract $5$ from $2$ .

$\frac{- x - 3}{2 x^{2} - 10}$

Step 5

Simplify with factoring out.

Tap for more steps...

Step 5.1

Factor $2$ out of $2 x^{2} - 10$ .

Tap for more steps...

Step 5.1.1

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

$\frac{- x - 3}{2 (x^{2}) - 10}$

Step 5.1.2

Factor $2$ out of $- 10$ .

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

Step 5.1.3

Factor $2$ out of $2 x^{2} + 2 \cdot - 5$ .

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

Step 5.2

Factor $- 1$ out of $- x$ .

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

Step 5.3

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- (x) - 1 (3)}{2 (x^{2} - 5)}$

Step 5.4

Factor $- 1$ out of $- (x) - 1 (3)$ .

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

Step 5.5

Simplify the expression.

Tap for more steps...

Step 5.5.1

Rewrite $- (x + 3)$ as $- 1 (x + 3)$ .

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

Step 5.5.2

Move the negative in front of the fraction.

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