Solve 3-a/2a-4div(a+2-5/a-2)

$$\frac { 3 - a } { 2 a - 4 } \div ( a + 2 - \frac { 5 } { a - 2 } )$$

Evaluate

$$-\frac{1}{2\left(a+3\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a+2 times \frac{a-2}{a-2}.

$$\frac{\frac{3-a}{2a-4}}{\frac{\left(a+2\right)\left(a-2\right)}{a-2}-\frac{5}{a-2}}$$

Since \frac{\left(a+2\right)\left(a-2\right)}{a-2} and \frac{5}{a-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3-a}{2a-4}}{\frac{\left(a+2\right)\left(a-2\right)-5}{a-2}}$$

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

$$\frac{\frac{3-a}{2a-4}}{\frac{a^{2}-2a+2a-4-5}{a-2}}$$

Combine like terms in a^{2}-2a+2a-4-5.

$$\frac{\frac{3-a}{2a-4}}{\frac{a^{2}-9}{a-2}}$$

Divide \frac{3-a}{2a-4} by \frac{a^{2}-9}{a-2} by multiplying \frac{3-a}{2a-4} by the reciprocal of \frac{a^{2}-9}{a-2}.

$$\frac{\left(3-a\right)\left(a-2\right)}{\left(2a-4\right)\left(a^{2}-9\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-2\right)\left(-a+3\right)}{2\left(a-3\right)\left(a-2\right)\left(a+3\right)}$$

Extract the negative sign in 3-a.

$$\frac{-\left(a-3\right)\left(a-2\right)}{2\left(a-3\right)\left(a-2\right)\left(a+3\right)}$$

Cancel out \left(a-3\right)\left(a-2\right) in both numerator and denominator.

$$\frac{-1}{2\left(a+3\right)}$$

Expand the expression.

$$\frac{-1}{2a+6}$$

Expand

$$-\frac{1}{2\left(a+3\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a+2 times \frac{a-2}{a-2}.

$$\frac{\frac{3-a}{2a-4}}{\frac{\left(a+2\right)\left(a-2\right)}{a-2}-\frac{5}{a-2}}$$

Since \frac{\left(a+2\right)\left(a-2\right)}{a-2} and \frac{5}{a-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3-a}{2a-4}}{\frac{\left(a+2\right)\left(a-2\right)-5}{a-2}}$$

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

$$\frac{\frac{3-a}{2a-4}}{\frac{a^{2}-2a+2a-4-5}{a-2}}$$

Combine like terms in a^{2}-2a+2a-4-5.

$$\frac{\frac{3-a}{2a-4}}{\frac{a^{2}-9}{a-2}}$$

Divide \frac{3-a}{2a-4} by \frac{a^{2}-9}{a-2} by multiplying \frac{3-a}{2a-4} by the reciprocal of \frac{a^{2}-9}{a-2}.

$$\frac{\left(3-a\right)\left(a-2\right)}{\left(2a-4\right)\left(a^{2}-9\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-2\right)\left(-a+3\right)}{2\left(a-3\right)\left(a-2\right)\left(a+3\right)}$$

Extract the negative sign in 3-a.

$$\frac{-\left(a-3\right)\left(a-2\right)}{2\left(a-3\right)\left(a-2\right)\left(a+3\right)}$$

Cancel out \left(a-3\right)\left(a-2\right) in both numerator and denominator.

$$\frac{-1}{2\left(a+3\right)}$$

Expand the expression.

$$\frac{-1}{2a+6}$$