Solve 3+2+2u^2+4u/1+u^2+1-u^2/1+u^2

$$3 + \frac { 2 + 2 u ^ { 2 } + 4 u } { 1 + u ^ { 2 } } + \frac { 1 - u ^ { 2 } } { 1 + u ^ { 2 } }$$

Evaluate

$$\frac{2\left(2u^{2}+2u+3\right)}{u^{2}+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{1+u^{2}}{1+u^{2}}.

$$\frac{3\left(1+u^{2}\right)}{1+u^{2}}+\frac{2+2u^{2}+4u}{1+u^{2}}+\frac{1-u^{2}}{1+u^{2}}$$

Since \frac{3\left(1+u^{2}\right)}{1+u^{2}} and \frac{2+2u^{2}+4u}{1+u^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3\left(1+u^{2}\right)+2+2u^{2}+4u}{1+u^{2}}+\frac{1-u^{2}}{1+u^{2}}$$

Do the multiplications in 3\left(1+u^{2}\right)+2+2u^{2}+4u.

$$\frac{3+3u^{2}+2+2u^{2}+4u}{1+u^{2}}+\frac{1-u^{2}}{1+u^{2}}$$

Combine like terms in 3+3u^{2}+2+2u^{2}+4u.

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

Since \frac{5+5u^{2}+4u}{1+u^{2}} and \frac{1-u^{2}}{1+u^{2}} have the same denominator, add them by adding their numerators.

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

Combine like terms in 5+5u^{2}+4u+1-u^{2}.

$$\frac{6+4u^{2}+4u}{1+u^{2}}$$

Expand

$$\frac{2\left(2u^{2}+2u+3\right)}{u^{2}+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{1+u^{2}}{1+u^{2}}.

$$\frac{3\left(1+u^{2}\right)}{1+u^{2}}+\frac{2+2u^{2}+4u}{1+u^{2}}+\frac{1-u^{2}}{1+u^{2}}$$

Since \frac{3\left(1+u^{2}\right)}{1+u^{2}} and \frac{2+2u^{2}+4u}{1+u^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3\left(1+u^{2}\right)+2+2u^{2}+4u}{1+u^{2}}+\frac{1-u^{2}}{1+u^{2}}$$

Do the multiplications in 3\left(1+u^{2}\right)+2+2u^{2}+4u.

$$\frac{3+3u^{2}+2+2u^{2}+4u}{1+u^{2}}+\frac{1-u^{2}}{1+u^{2}}$$

Combine like terms in 3+3u^{2}+2+2u^{2}+4u.

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

Since \frac{5+5u^{2}+4u}{1+u^{2}} and \frac{1-u^{2}}{1+u^{2}} have the same denominator, add them by adding their numerators.

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

Combine like terms in 5+5u^{2}+4u+1-u^{2}.

$$\frac{6+4u^{2}+4u}{1+u^{2}}$$