Solve (2/9z^2+1/3z^2):(5/6z-4/3z)=

$$( \frac { 2 } { 9 } z ^ { 2 } + \frac { 1 } { 3 } z ^ { 2 } ) : ( \frac { 5 } { 6 } z - \frac { 4 } { 3 } z ) =$$

Evaluate

$$-\frac{10z}{9}$$

Solution Steps

Combine \frac{2}{9}z^{2} and \frac{1}{3}z^{2} to get \frac{5}{9}z^{2}.

$$\frac{\frac{5}{9}z^{2}}{\frac{5}{6}z-\frac{4}{3}z}$$

Combine \frac{5}{6}z and -\frac{4}{3}z to get -\frac{1}{2}z.

$$\frac{\frac{5}{9}z^{2}}{-\frac{1}{2}z}$$

Cancel out z in both numerator and denominator.

$$\frac{\frac{5}{9}z}{-\frac{1}{2}}$$

Divide \frac{5}{9}z by -\frac{1}{2} by multiplying \frac{5}{9}z by the reciprocal of -\frac{1}{2}.

$$\frac{\frac{5}{9}z\times 2}{-1}$$

Multiply \frac{5}{9} and 2 to get \frac{10}{9}.

$$\frac{\frac{10}{9}z}{-1}$$

Anything divided by -1 gives its opposite.

$$-\frac{10}{9}z$$

Expand

$$-\frac{10z}{9}$$

Solution Steps

Combine \frac{2}{9}z^{2} and \frac{1}{3}z^{2} to get \frac{5}{9}z^{2}.

$$\frac{\frac{5}{9}z^{2}}{\frac{5}{6}z-\frac{4}{3}z}$$

Combine \frac{5}{6}z and -\frac{4}{3}z to get -\frac{1}{2}z.

$$\frac{\frac{5}{9}z^{2}}{-\frac{1}{2}z}$$

Cancel out z in both numerator and denominator.

$$\frac{\frac{5}{9}z}{-\frac{1}{2}}$$

Divide \frac{5}{9}z by -\frac{1}{2} by multiplying \frac{5}{9}z by the reciprocal of -\frac{1}{2}.

$$\frac{\frac{5}{9}z\times 2}{-1}$$

Multiply \frac{5}{9} and 2 to get \frac{10}{9}.

$$\frac{\frac{10}{9}z}{-1}$$

Anything divided by -1 gives its opposite.

$$-\frac{10}{9}z$$