Solve c/d-d/c/frac{d{c}+4}

$$\frac { \frac { c } { d } - \frac { d } { c } } { \frac { d } { c } + 4 }$$

Evaluate

$$\frac{c^{2}-d^{2}}{d\left(4c+d\right)}$$

Short Solution Steps

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

$$\frac{\frac{cc}{cd}-\frac{dd}{cd}}{\frac{d}{c}+4}$$

Since \frac{cc}{cd} and \frac{dd}{cd} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{cc-dd}{cd}}{\frac{d}{c}+4}$$

Do the multiplications in cc-dd.

$$\frac{\frac{c^{2}-d^{2}}{cd}}{\frac{d}{c}+4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{c}{c}.

$$\frac{\frac{c^{2}-d^{2}}{cd}}{\frac{d}{c}+\frac{4c}{c}}$$

Since \frac{d}{c} and \frac{4c}{c} have the same denominator, add them by adding their numerators.

$$\frac{\frac{c^{2}-d^{2}}{cd}}{\frac{d+4c}{c}}$$

Divide \frac{c^{2}-d^{2}}{cd} by \frac{d+4c}{c} by multiplying \frac{c^{2}-d^{2}}{cd} by the reciprocal of \frac{d+4c}{c}.

$$\frac{\left(c^{2}-d^{2}\right)c}{cd\left(d+4c\right)}$$

Cancel out c in both numerator and denominator.

$$\frac{c^{2}-d^{2}}{d\left(4c+d\right)}$$

Use the distributive property to multiply d by 4c+d.

$$\frac{c^{2}-d^{2}}{4dc+d^{2}}$$

Expand

$$\frac{c^{2}-d^{2}}{d\left(4c+d\right)}$$

Short Solution Steps

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

$$\frac{\frac{cc}{cd}-\frac{dd}{cd}}{\frac{d}{c}+4}$$

Since \frac{cc}{cd} and \frac{dd}{cd} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{cc-dd}{cd}}{\frac{d}{c}+4}$$

Do the multiplications in cc-dd.

$$\frac{\frac{c^{2}-d^{2}}{cd}}{\frac{d}{c}+4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{c}{c}.

$$\frac{\frac{c^{2}-d^{2}}{cd}}{\frac{d}{c}+\frac{4c}{c}}$$

Since \frac{d}{c} and \frac{4c}{c} have the same denominator, add them by adding their numerators.

$$\frac{\frac{c^{2}-d^{2}}{cd}}{\frac{d+4c}{c}}$$

Divide \frac{c^{2}-d^{2}}{cd} by \frac{d+4c}{c} by multiplying \frac{c^{2}-d^{2}}{cd} by the reciprocal of \frac{d+4c}{c}.

$$\frac{\left(c^{2}-d^{2}\right)c}{cd\left(d+4c\right)}$$

Cancel out c in both numerator and denominator.

$$\frac{c^{2}-d^{2}}{d\left(4c+d\right)}$$

Use the distributive property to multiply d by 4c+d.

$$\frac{c^{2}-d^{2}}{4dc+d^{2}}$$