Solve t/t+4+8-t/t-16/t^2+4t

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

Evaluate

$$\frac{4}{t}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of t+4 and t is t\left(t+4\right). Multiply \frac{t}{t+4} times \frac{t}{t}. Multiply \frac{8-t}{t} times \frac{t+4}{t+4}.

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

Since \frac{tt}{t\left(t+4\right)} and \frac{\left(8-t\right)\left(t+4\right)}{t\left(t+4\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in tt+\left(8-t\right)\left(t+4\right).

$$\frac{t^{2}+8t+32-t^{2}-4t}{t\left(t+4\right)}-\frac{16}{t^{2}+4t}$$

Combine like terms in t^{2}+8t+32-t^{2}-4t.

$$\frac{4t+32}{t\left(t+4\right)}-\frac{16}{t^{2}+4t}$$

Factor t^{2}+4t.

$$\frac{4t+32}{t\left(t+4\right)}-\frac{16}{t\left(t+4\right)}$$

Since \frac{4t+32}{t\left(t+4\right)} and \frac{16}{t\left(t+4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4t+32-16}{t\left(t+4\right)}$$

Combine like terms in 4t+32-16.

$$\frac{4t+16}{t\left(t+4\right)}$$

Factor the expressions that are not already factored in \frac{4t+16}{t\left(t+4\right)}.

$$\frac{4\left(t+4\right)}{t\left(t+4\right)}$$

Cancel out t+4 in both numerator and denominator.

$$\frac{4}{t}$$

Expand

$$\frac{4}{t}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of t+4 and t is t\left(t+4\right). Multiply \frac{t}{t+4} times \frac{t}{t}. Multiply \frac{8-t}{t} times \frac{t+4}{t+4}.

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

Since \frac{tt}{t\left(t+4\right)} and \frac{\left(8-t\right)\left(t+4\right)}{t\left(t+4\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in tt+\left(8-t\right)\left(t+4\right).

$$\frac{t^{2}+8t+32-t^{2}-4t}{t\left(t+4\right)}-\frac{16}{t^{2}+4t}$$

Combine like terms in t^{2}+8t+32-t^{2}-4t.

$$\frac{4t+32}{t\left(t+4\right)}-\frac{16}{t^{2}+4t}$$

Factor t^{2}+4t.

$$\frac{4t+32}{t\left(t+4\right)}-\frac{16}{t\left(t+4\right)}$$

Since \frac{4t+32}{t\left(t+4\right)} and \frac{16}{t\left(t+4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4t+32-16}{t\left(t+4\right)}$$

Combine like terms in 4t+32-16.

$$\frac{4t+16}{t\left(t+4\right)}$$

Factor the expressions that are not already factored in \frac{4t+16}{t\left(t+4\right)}.

$$\frac{4\left(t+4\right)}{t\left(t+4\right)}$$

Cancel out t+4 in both numerator and denominator.

$$\frac{4}{t}$$