Solve 3d/d^2-c^2-3c/c^2-d^2

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

Evaluate

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

Short Solution Steps

Factor d^{2}-c^{2}. Factor c^{2}-d^{2}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(c+d\right)\left(-c+d\right) and \left(c+d\right)\left(c-d\right) is \left(c+d\right)\left(c-d\right). Multiply \frac{3d}{\left(c+d\right)\left(-c+d\right)} times \frac{-1}{-1}.

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

Since \frac{-3d}{\left(c+d\right)\left(c-d\right)} and \frac{3c}{\left(c+d\right)\left(c-d\right)} have the same denominator, subtract them by subtracting their numerators.

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

Factor the expressions that are not already factored in \frac{-3d-3c}{\left(c+d\right)\left(c-d\right)}.

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

Extract the negative sign in -d-c.

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

Cancel out c+d in both numerator and denominator.

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

Factor

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