Solve t^2+4/t^2+t-t+4/t

$$\frac { t ^ { 2 } + 4 } { t ^ { 2 } + t } - \frac { t + 4 } { t }$$

Evaluate

$$-\frac{5}{t+1}$$

Short Solution Steps

Factor t^{2}+t.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of t\left(t+1\right) and t is t\left(t+1\right). Multiply \frac{t+4}{t} times \frac{t+1}{t+1}.

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

Since \frac{t^{2}+4}{t\left(t+1\right)} and \frac{\left(t+4\right)\left(t+1\right)}{t\left(t+1\right)} have the same denominator, subtract them by subtracting their numerators.

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

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

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

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

$$\frac{-5t}{t\left(t+1\right)}$$

Cancel out t in both numerator and denominator.

$$\frac{-5}{t+1}$$

Expand

$$-\frac{5}{t+1}$$

Short Solution Steps

Factor t^{2}+t.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of t\left(t+1\right) and t is t\left(t+1\right). Multiply \frac{t+4}{t} times \frac{t+1}{t+1}.

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

Since \frac{t^{2}+4}{t\left(t+1\right)} and \frac{\left(t+4\right)\left(t+1\right)}{t\left(t+1\right)} have the same denominator, subtract them by subtracting their numerators.

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

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

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

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

$$\frac{-5t}{t\left(t+1\right)}$$

Cancel out t in both numerator and denominator.

$$\frac{-5}{t+1}$$