Solve c/2ddiv(c/2d-c/3)

$$\frac { c } { 2 d } \div ( \frac { c } { 2 d } - \frac { c } { 3 } )$$

Evaluate

$$-\frac{3}{2d-3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2d and 3 is 6d. Multiply \frac{c}{2d} times \frac{3}{3}. Multiply \frac{c}{3} times \frac{2d}{2d}.

$$\frac{\frac{c}{2d}}{\frac{3c}{6d}-\frac{c\times 2d}{6d}}$$

Since \frac{3c}{6d} and \frac{c\times 2d}{6d} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{c}{2d}}{\frac{3c-c\times 2d}{6d}}$$

Do the multiplications in 3c-c\times 2d.

$$\frac{\frac{c}{2d}}{\frac{3c-2cd}{6d}}$$

Divide \frac{c}{2d} by \frac{3c-2cd}{6d} by multiplying \frac{c}{2d} by the reciprocal of \frac{3c-2cd}{6d}.

$$\frac{c\times 6d}{2d\left(3c-2cd\right)}$$

Cancel out 2d in both numerator and denominator.

$$\frac{3c}{-2cd+3c}$$

Factor the expressions that are not already factored.

$$\frac{3c}{c\left(-2d+3\right)}$$

Cancel out c in both numerator and denominator.

$$\frac{3}{-2d+3}$$

Differentiate w.r.t. d

$$\frac{6}{\left(2d-3\right)^{2}}$$