Simplify (1/2-(x+5)/4)/((x^2)/2-5/2)

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

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

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

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $4$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

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

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

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $- 5$ .

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $- 1$ by $5$ .

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

Subtract $5$ from $2$ .

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

Simplify with factoring out.

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

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

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

Factor $2$ out of $- 10$ .

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

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

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

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

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

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

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

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

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

Simplify the expression.

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

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

Move the negative in front of the fraction.

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

Simplify (1/2-(x+5)/4)/((x^2)/2-5/2)

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