Solve 5/2-9/2*(1/3-2/3)^2+(frac{1}{3})^-1

$$\frac { 5 } { 2 } - \frac { 9 } { 2 } \cdot ( \frac { 1 } { 3 } - \frac { 2 } { 3 } ) ^ { 2 } + ( \frac { 1 } { 3 } ) ^ { - 1 }$$

Evaluate

$$5$$

Solution Steps

Subtract \frac{2}{3} from \frac{1}{3} to get -\frac{1}{3}.

$$\frac{5}{2}-\frac{9}{2}\left(-\frac{1}{3}\right)^{2}+\left(\frac{1}{3}\right)^{-1}$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{5}{2}-\frac{9}{2}\times \frac{1}{9}+\left(\frac{1}{3}\right)^{-1}$$

Multiply \frac{9}{2} and \frac{1}{9} to get \frac{1}{2}.

$$\frac{5}{2}-\frac{1}{2}+\left(\frac{1}{3}\right)^{-1}$$

Subtract \frac{1}{2} from \frac{5}{2} to get 2.

$$2+\left(\frac{1}{3}\right)^{-1}$$

Calculate \frac{1}{3} to the power of -1 and get 3.

$$2+3$$

Add 2 and 3 to get 5.

$$5$$

Factor

$$5$$