Solve (-a^{2}b^{3}c+2/5a^{2}b^{3}c)+(2/5a^{5}b^{3}c^{2}+1/3a^{5}b^{3}c^{2}):(-5/2a^3c+frac{3}{10}a^3c)]:[(-frac{5}{8}a)(-frac{4}{3}b^2)-frac{1}{4}ab^2]

$$( - a ^ { 2 } b ^ { 3 } c + \frac { 2 } { 5 } a ^ { 2 } b ^ { 3 } c ) + ( \frac { 2 } { 5 } a ^ { 5 } b ^ { 3 } c ^ { 2 } + \frac { 1 } { 3 } a ^ { 5 } b ^ { 3 } c ^ { 2 } ) : ( - \frac { 5 } { 2 } a ^ { 3 } c + \frac { 3 } { 10 } a ^ { 3 } c ) ] : [ ( - \frac { 5 } { 8 } a ) ( - \frac { 4 } { 3 } b ^ { 2 } ) - \frac { 1 } { 4 } a b ^ { 2 } ]$$

Evaluate

$$-\frac{14ca^{2}b^{3}}{15}$$

Solution Steps

Combine \frac{2}{5}a^{5}b^{3}c^{2} and \frac{1}{3}a^{5}b^{3}c^{2} to get \frac{11}{15}a^{5}b^{3}c^{2}.

$$\left(-a^{2}\right)b^{3}c+\frac{2}{5}a^{2}b^{3}c+\frac{\frac{11}{15}a^{5}b^{3}c^{2}}{-\frac{5}{2}a^{3}c+\frac{3}{10}a^{3}c}$$

Combine -\frac{5}{2}a^{3}c and \frac{3}{10}a^{3}c to get -\frac{11}{5}a^{3}c.

$$\left(-a^{2}\right)b^{3}c+\frac{2}{5}a^{2}b^{3}c+\frac{\frac{11}{15}a^{5}b^{3}c^{2}}{-\frac{11}{5}a^{3}c}$$

Cancel out ca^{3} in both numerator and denominator.

$$\left(-a^{2}\right)b^{3}c+\frac{2}{5}a^{2}b^{3}c+\frac{\frac{11}{15}ca^{2}b^{3}}{-\frac{11}{5}}$$

Divide \frac{11}{15}ca^{2}b^{3} by -\frac{11}{5} by multiplying \frac{11}{15}ca^{2}b^{3} by the reciprocal of -\frac{11}{5}.

$$\left(-a^{2}\right)b^{3}c+\frac{2}{5}a^{2}b^{3}c+\frac{\frac{11}{15}ca^{2}b^{3}\times 5}{-11}$$

Multiply \frac{11}{15} and 5 to get \frac{11}{3}.

$$\left(-a^{2}\right)b^{3}c+\frac{2}{5}a^{2}b^{3}c+\frac{\frac{11}{3}ca^{2}b^{3}}{-11}$$

Divide \frac{11}{3}ca^{2}b^{3} by -11 to get -\frac{1}{3}ca^{2}b^{3}.

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

Combine \frac{2}{5}a^{2}b^{3}c and -\frac{1}{3}ca^{2}b^{3} to get \frac{1}{15}a^{2}b^{3}c.

$$\left(-a^{2}\right)b^{3}c+\frac{1}{15}a^{2}b^{3}c$$

Combine -a^{2}b^{3}c and \frac{1}{15}a^{2}b^{3}c to get -\frac{14}{15}a^{2}b^{3}c.

$$-\frac{14}{15}a^{2}b^{3}c$$

Expand

$$-\frac{14ca^{2}b^{3}}{15}$$

Solution Steps

Combine \frac{2}{5}a^{5}b^{3}c^{2} and \frac{1}{3}a^{5}b^{3}c^{2} to get \frac{11}{15}a^{5}b^{3}c^{2}.

$$\left(-a^{2}\right)b^{3}c+\frac{2}{5}a^{2}b^{3}c+\frac{\frac{11}{15}a^{5}b^{3}c^{2}}{-\frac{5}{2}a^{3}c+\frac{3}{10}a^{3}c}$$

Combine -\frac{5}{2}a^{3}c and \frac{3}{10}a^{3}c to get -\frac{11}{5}a^{3}c.

$$\left(-a^{2}\right)b^{3}c+\frac{2}{5}a^{2}b^{3}c+\frac{\frac{11}{15}a^{5}b^{3}c^{2}}{-\frac{11}{5}a^{3}c}$$

Cancel out ca^{3} in both numerator and denominator.

$$\left(-a^{2}\right)b^{3}c+\frac{2}{5}a^{2}b^{3}c+\frac{\frac{11}{15}ca^{2}b^{3}}{-\frac{11}{5}}$$

Divide \frac{11}{15}ca^{2}b^{3} by -\frac{11}{5} by multiplying \frac{11}{15}ca^{2}b^{3} by the reciprocal of -\frac{11}{5}.

$$\left(-a^{2}\right)b^{3}c+\frac{2}{5}a^{2}b^{3}c+\frac{\frac{11}{15}ca^{2}b^{3}\times 5}{-11}$$

Multiply \frac{11}{15} and 5 to get \frac{11}{3}.

$$\left(-a^{2}\right)b^{3}c+\frac{2}{5}a^{2}b^{3}c+\frac{\frac{11}{3}ca^{2}b^{3}}{-11}$$

Divide \frac{11}{3}ca^{2}b^{3} by -11 to get -\frac{1}{3}ca^{2}b^{3}.

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

Combine \frac{2}{5}a^{2}b^{3}c and -\frac{1}{3}ca^{2}b^{3} to get \frac{1}{15}a^{2}b^{3}c.

$$\left(-a^{2}\right)b^{3}c+\frac{1}{15}a^{2}b^{3}c$$

Combine -a^{2}b^{3}c and \frac{1}{15}a^{2}b^{3}c to get -\frac{14}{15}a^{2}b^{3}c.

$$-\frac{14}{15}a^{2}b^{3}c$$