Solve t/(1+t)+2/(1+t)^2

$$\frac { t } { ( 1 + t ) } + \frac { 2 } { ( 1 + t ) ^ { 2 } }$$

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in t\left(t+1\right)+2.

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

Expand \left(t+1\right)^{2}.

$$\frac{t^{2}+t+2}{t^{2}+2t+1}$$

Expand

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

Short Solution Steps

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

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

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

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

Do the multiplications in t\left(t+1\right)+2.

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

Expand \left(t+1\right)^{2}.

$$\frac{t^{2}+t+2}{t^{2}+2t+1}$$