Solve 3b^2/16adivbc/2a^2*(-2a/b)

$$\frac { 3 b ^ { 2 } } { 16 a } \div \frac { b c } { 2 a ^ { 2 } } \cdot ( - \frac { 2 a } { b } )$$

Evaluate

$$-\frac{3a^{2}}{4c}$$

Solution Steps

Divide \frac{3b^{2}}{16a} by \frac{bc}{2a^{2}} by multiplying \frac{3b^{2}}{16a} by the reciprocal of \frac{bc}{2a^{2}}.

$$\frac{3b^{2}\times 2a^{2}}{16abc}\left(-\frac{2a}{b}\right)$$

Cancel out 2ab in both numerator and denominator.

$$\frac{3ab}{8c}\left(-\frac{2a}{b}\right)$$

Multiply \frac{3ab}{8c} times -\frac{2a}{b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3ab\times 2a}{8cb}$$

Cancel out 2b in both numerator and denominator.

$$\frac{-3aa}{4c}$$

Multiply a and a to get a^{2}.

$$\frac{-3a^{2}}{4c}$$

Differentiate w.r.t. a

$$-\frac{3a}{2c}$$