Solve (-9/2abc^2):(-1/2abc)*(1/3a^2b)-10/3a^2bc

$$( - \frac { 9 } { 2 } a b c ^ { 2 } ) : ( - \frac { 1 } { 2 } a b c ) \cdot ( \frac { 1 } { 3 } a ^ { 2 } b ) - \frac { 10 } { 3 } a ^ { 2 } b c$$

Evaluate

$$-\frac{bca^{2}}{3}$$

Solution Steps

Cancel out abc in both numerator and denominator.

$$\frac{-\frac{9}{2}c}{-\frac{1}{2}}\times \frac{1}{3}a^{2}b-\frac{10}{3}a^{2}bc$$

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

$$\frac{-\frac{9}{2}c\times 2}{-1}\times \frac{1}{3}a^{2}b-\frac{10}{3}a^{2}bc$$

Anything divided by -1 gives its opposite.

$$\frac{9}{2}c\times 2\times \frac{1}{3}a^{2}b-\frac{10}{3}a^{2}bc$$

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

$$9c\times \frac{1}{3}a^{2}b-\frac{10}{3}a^{2}bc$$

Multiply 9 and \frac{1}{3} to get 3.

$$3ca^{2}b-\frac{10}{3}a^{2}bc$$

Combine 3ca^{2}b and -\frac{10}{3}a^{2}bc to get -\frac{1}{3}ca^{2}b.

$$-\frac{1}{3}ca^{2}b$$

Differentiate w.r.t. b

$$-\frac{ca^{2}}{3}$$