Solve t(3-t)/t-frac{t^2-t{2}}

$$\frac { t ( 3 - t ) } { t - \frac { t ^ { 2 } - t } { 2 } }$$

Evaluate

$$2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply t times \frac{2}{2}.

$$\frac{t\left(3-t\right)}{\frac{2t}{2}-\frac{t^{2}-t}{2}}$$

Since \frac{2t}{2} and \frac{t^{2}-t}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{t\left(3-t\right)}{\frac{2t-\left(t^{2}-t\right)}{2}}$$

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

$$\frac{t\left(3-t\right)}{\frac{2t-t^{2}+t}{2}}$$

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

$$\frac{t\left(3-t\right)}{\frac{3t-t^{2}}{2}}$$

Divide t\left(3-t\right) by \frac{3t-t^{2}}{2} by multiplying t\left(3-t\right) by the reciprocal of \frac{3t-t^{2}}{2}.

$$\frac{t\left(3-t\right)\times 2}{3t-t^{2}}$$

Factor the expressions that are not already factored.

$$\frac{2t\left(-t+3\right)}{t\left(-t+3\right)}$$

Cancel out t\left(-t+3\right) in both numerator and denominator.

$$2$$

Factor

$$2$$