Solve 1/2-x+5/4/frac{x^2{2}-5/2}

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{1}{2} times \frac{2}{2}.

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

Since \frac{2}{4} and \frac{x+5}{4} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2-\left(x+5\right).

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

Combine like terms in 2-x-5.

$$\frac{\frac{-3-x}{4}}{\frac{x^{2}}{2}-\frac{5}{2}}$$

Since \frac{x^{2}}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-3-x}{4}}{\frac{x^{2}-5}{2}}$$

Divide \frac{-3-x}{4} by \frac{x^{2}-5}{2} by multiplying \frac{-3-x}{4} by the reciprocal of \frac{x^{2}-5}{2}.

$$\frac{\left(-3-x\right)\times 2}{4\left(x^{2}-5\right)}$$

Cancel out 2 in both numerator and denominator.

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

Use the distributive property to multiply 2 by x^{2}-5.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{1}{2} times \frac{2}{2}.

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

Since \frac{2}{4} and \frac{x+5}{4} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2-\left(x+5\right).

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

Combine like terms in 2-x-5.

$$\frac{\frac{-3-x}{4}}{\frac{x^{2}}{2}-\frac{5}{2}}$$

Since \frac{x^{2}}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-3-x}{4}}{\frac{x^{2}-5}{2}}$$

Divide \frac{-3-x}{4} by \frac{x^{2}-5}{2} by multiplying \frac{-3-x}{4} by the reciprocal of \frac{x^{2}-5}{2}.

$$\frac{\left(-3-x\right)\times 2}{4\left(x^{2}-5\right)}$$

Cancel out 2 in both numerator and denominator.

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

Use the distributive property to multiply 2 by x^{2}-5.

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