Solve 2-2/u+2/frac{1{u+2}+u/2}

$$\frac { 2 - \frac { 2 } { u + 2 } } { \frac { 1 } { u + 2 } + \frac { u } { 2 } }$$

Evaluate

$$\frac{4\left(u+1\right)}{u^{2}+2u+2}$$

Short Solution Steps

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

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

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

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

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

$$\frac{\frac{2u+4-2}{u+2}}{\frac{1}{u+2}+\frac{u}{2}}$$

Combine like terms in 2u+4-2.

$$\frac{\frac{2u+2}{u+2}}{\frac{1}{u+2}+\frac{u}{2}}$$

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

$$\frac{\frac{2u+2}{u+2}}{\frac{2}{2\left(u+2\right)}+\frac{u\left(u+2\right)}{2\left(u+2\right)}}$$

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

$$\frac{\frac{2u+2}{u+2}}{\frac{2+u\left(u+2\right)}{2\left(u+2\right)}}$$

Do the multiplications in 2+u\left(u+2\right).

$$\frac{\frac{2u+2}{u+2}}{\frac{2+u^{2}+2u}{2\left(u+2\right)}}$$

Divide \frac{2u+2}{u+2} by \frac{2+u^{2}+2u}{2\left(u+2\right)} by multiplying \frac{2u+2}{u+2} by the reciprocal of \frac{2+u^{2}+2u}{2\left(u+2\right)}.

$$\frac{\left(2u+2\right)\times 2\left(u+2\right)}{\left(u+2\right)\left(2+u^{2}+2u\right)}$$

Cancel out u+2 in both numerator and denominator.

$$\frac{2\left(2u+2\right)}{u^{2}+2u+2}$$

Use the distributive property to multiply 2 by 2u+2.

$$\frac{4u+4}{u^{2}+2u+2}$$

Expand

$$\frac{4\left(u+1\right)}{u^{2}+2u+2}$$

Short Solution Steps

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

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

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

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

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

$$\frac{\frac{2u+4-2}{u+2}}{\frac{1}{u+2}+\frac{u}{2}}$$

Combine like terms in 2u+4-2.

$$\frac{\frac{2u+2}{u+2}}{\frac{1}{u+2}+\frac{u}{2}}$$

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

$$\frac{\frac{2u+2}{u+2}}{\frac{2}{2\left(u+2\right)}+\frac{u\left(u+2\right)}{2\left(u+2\right)}}$$

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

$$\frac{\frac{2u+2}{u+2}}{\frac{2+u\left(u+2\right)}{2\left(u+2\right)}}$$

Do the multiplications in 2+u\left(u+2\right).

$$\frac{\frac{2u+2}{u+2}}{\frac{2+u^{2}+2u}{2\left(u+2\right)}}$$

Divide \frac{2u+2}{u+2} by \frac{2+u^{2}+2u}{2\left(u+2\right)} by multiplying \frac{2u+2}{u+2} by the reciprocal of \frac{2+u^{2}+2u}{2\left(u+2\right)}.

$$\frac{\left(2u+2\right)\times 2\left(u+2\right)}{\left(u+2\right)\left(2+u^{2}+2u\right)}$$

Cancel out u+2 in both numerator and denominator.

$$\frac{2\left(2u+2\right)}{u^{2}+2u+2}$$

Use the distributive property to multiply 2 by 2u+2.

$$\frac{4u+4}{u^{2}+2u+2}$$