Solve a^2/4-4/frac{a^2{8}-a+2}

$$\frac { \frac { a ^ { 2 } } { 4 } - 4 } { \frac { a ^ { 2 } } { 8 } - a + 2 }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{4}{4}.

$$\frac{\frac{a^{2}}{4}-\frac{4\times 4}{4}}{\frac{a^{2}}{8}-a+2}$$

Since \frac{a^{2}}{4} and \frac{4\times 4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{a^{2}-4\times 4}{4}}{\frac{a^{2}}{8}-a+2}$$

Do the multiplications in a^{2}-4\times 4.

$$\frac{\frac{a^{2}-16}{4}}{\frac{a^{2}}{8}-a+2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -a+2 times \frac{8}{8}.

$$\frac{\frac{a^{2}-16}{4}}{\frac{a^{2}}{8}+\frac{8\left(-a+2\right)}{8}}$$

Since \frac{a^{2}}{8} and \frac{8\left(-a+2\right)}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{a^{2}-16}{4}}{\frac{a^{2}+8\left(-a+2\right)}{8}}$$

Do the multiplications in a^{2}+8\left(-a+2\right).

$$\frac{\frac{a^{2}-16}{4}}{\frac{a^{2}-8a+16}{8}}$$

Divide \frac{a^{2}-16}{4} by \frac{a^{2}-8a+16}{8} by multiplying \frac{a^{2}-16}{4} by the reciprocal of \frac{a^{2}-8a+16}{8}.

$$\frac{\left(a^{2}-16\right)\times 8}{4\left(a^{2}-8a+16\right)}$$

Cancel out 4 in both numerator and denominator.

$$\frac{2\left(a^{2}-16\right)}{a^{2}-8a+16}$$

Factor the expressions that are not already factored.

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

Cancel out a-4 in both numerator and denominator.

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

Expand the expression.

$$\frac{2a+8}{a-4}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{4}{4}.

$$\frac{\frac{a^{2}}{4}-\frac{4\times 4}{4}}{\frac{a^{2}}{8}-a+2}$$

Since \frac{a^{2}}{4} and \frac{4\times 4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{a^{2}-4\times 4}{4}}{\frac{a^{2}}{8}-a+2}$$

Do the multiplications in a^{2}-4\times 4.

$$\frac{\frac{a^{2}-16}{4}}{\frac{a^{2}}{8}-a+2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -a+2 times \frac{8}{8}.

$$\frac{\frac{a^{2}-16}{4}}{\frac{a^{2}}{8}+\frac{8\left(-a+2\right)}{8}}$$

Since \frac{a^{2}}{8} and \frac{8\left(-a+2\right)}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{a^{2}-16}{4}}{\frac{a^{2}+8\left(-a+2\right)}{8}}$$

Do the multiplications in a^{2}+8\left(-a+2\right).

$$\frac{\frac{a^{2}-16}{4}}{\frac{a^{2}-8a+16}{8}}$$

Divide \frac{a^{2}-16}{4} by \frac{a^{2}-8a+16}{8} by multiplying \frac{a^{2}-16}{4} by the reciprocal of \frac{a^{2}-8a+16}{8}.

$$\frac{\left(a^{2}-16\right)\times 8}{4\left(a^{2}-8a+16\right)}$$

Cancel out 4 in both numerator and denominator.

$$\frac{2\left(a^{2}-16\right)}{a^{2}-8a+16}$$

Factor the expressions that are not already factored.

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

Cancel out a-4 in both numerator and denominator.

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

Expand the expression.

$$\frac{2a+8}{a-4}$$