Solve (-12a^{4}b^3):(-3ab^2)-(-45a^3b^2):(-9b)

$$( - 12 a ^ { 4 } b ^ { 3 } ) : ( - 3 a b ^ { 2 } ) - ( - 45 a ^ { 3 } b ^ { 2 } ) : ( - 9 b )$$

Evaluate

$$-ba^{3}$$

Solution Steps

Cancel out 3ab^{2} in both numerator and denominator.

$$\frac{-4ba^{3}}{-1}-\frac{-45a^{3}b^{2}}{-9b}$$

Anything divided by -1 gives its opposite.

$$4ba^{3}-\frac{-45a^{3}b^{2}}{-9b}$$

Cancel out 9b in both numerator and denominator.

$$4ba^{3}-\frac{-5ba^{3}}{-1}$$

Anything divided by -1 gives its opposite.

$$4ba^{3}-5ba^{3}$$

Combine 4ba^{3} and -5ba^{3} to get -ba^{3}.

$$-ba^{3}$$

Differentiate w.r.t. b

$$-a^{3}$$