Solve 2-t/t-5+2+t/t+5

$$\frac { 2 - t } { t - 5 } + \frac { 2 + t } { t + 5 }$$

Evaluate

$$-\frac{6t}{t^{2}-25}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of t-5 and t+5 is \left(t-5\right)\left(t+5\right). Multiply \frac{2-t}{t-5} times \frac{t+5}{t+5}. Multiply \frac{2+t}{t+5} times \frac{t-5}{t-5}.

$$\frac{\left(2-t\right)\left(t+5\right)}{\left(t-5\right)\left(t+5\right)}+\frac{\left(2+t\right)\left(t-5\right)}{\left(t-5\right)\left(t+5\right)}$$

Since \frac{\left(2-t\right)\left(t+5\right)}{\left(t-5\right)\left(t+5\right)} and \frac{\left(2+t\right)\left(t-5\right)}{\left(t-5\right)\left(t+5\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(2-t\right)\left(t+5\right)+\left(2+t\right)\left(t-5\right)}{\left(t-5\right)\left(t+5\right)}$$

Do the multiplications in \left(2-t\right)\left(t+5\right)+\left(2+t\right)\left(t-5\right).

$$\frac{2t+10-t^{2}-5t+2t-10+t^{2}-5t}{\left(t-5\right)\left(t+5\right)}$$

Combine like terms in 2t+10-t^{2}-5t+2t-10+t^{2}-5t.

$$\frac{-6t}{\left(t-5\right)\left(t+5\right)}$$

Expand \left(t-5\right)\left(t+5\right).

$$\frac{-6t}{t^{2}-25}$$

Expand

$$-\frac{6t}{t^{2}-25}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of t-5 and t+5 is \left(t-5\right)\left(t+5\right). Multiply \frac{2-t}{t-5} times \frac{t+5}{t+5}. Multiply \frac{2+t}{t+5} times \frac{t-5}{t-5}.

$$\frac{\left(2-t\right)\left(t+5\right)}{\left(t-5\right)\left(t+5\right)}+\frac{\left(2+t\right)\left(t-5\right)}{\left(t-5\right)\left(t+5\right)}$$

Since \frac{\left(2-t\right)\left(t+5\right)}{\left(t-5\right)\left(t+5\right)} and \frac{\left(2+t\right)\left(t-5\right)}{\left(t-5\right)\left(t+5\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(2-t\right)\left(t+5\right)+\left(2+t\right)\left(t-5\right)}{\left(t-5\right)\left(t+5\right)}$$

Do the multiplications in \left(2-t\right)\left(t+5\right)+\left(2+t\right)\left(t-5\right).

$$\frac{2t+10-t^{2}-5t+2t-10+t^{2}-5t}{\left(t-5\right)\left(t+5\right)}$$

Combine like terms in 2t+10-t^{2}-5t+2t-10+t^{2}-5t.

$$\frac{-6t}{\left(t-5\right)\left(t+5\right)}$$

Expand \left(t-5\right)\left(t+5\right).

$$\frac{-6t}{t^{2}-25}$$