Solve 1/d-d/c/frac{1{c}+6}

$$\frac{ \frac{ 1 }{ d } - \frac{ d }{ c } }{ \frac{ 1 }{ c } +6 }$$

Evaluate

$$\frac{c-d^{2}}{d\left(6c+1\right)}$$

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{1}{d} times \frac{c}{c}. Multiply \frac{d}{c} times \frac{d}{d}.

$$\frac{\frac{c}{cd}-\frac{dd}{cd}}{\frac{1}{c}+6}$$

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

$$\frac{\frac{c-dd}{cd}}{\frac{1}{c}+6}$$

Do the multiplications in c-dd.

$$\frac{\frac{c-d^{2}}{cd}}{\frac{1}{c}+6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{c}{c}.

$$\frac{\frac{c-d^{2}}{cd}}{\frac{1}{c}+\frac{6c}{c}}$$

Since \frac{1}{c} and \frac{6c}{c} have the same denominator, add them by adding their numerators.

$$\frac{\frac{c-d^{2}}{cd}}{\frac{1+6c}{c}}$$

Divide \frac{c-d^{2}}{cd} by \frac{1+6c}{c} by multiplying \frac{c-d^{2}}{cd} by the reciprocal of \frac{1+6c}{c}.

$$\frac{\left(c-d^{2}\right)c}{cd\left(1+6c\right)}$$

Cancel out c in both numerator and denominator.

$$\frac{c-d^{2}}{d\left(6c+1\right)}$$

Use the distributive property to multiply d by 6c+1.

$$\frac{c-d^{2}}{6dc+d}$$

Expand

$$\frac{c-d^{2}}{d\left(6c+1\right)}$$

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{1}{d} times \frac{c}{c}. Multiply \frac{d}{c} times \frac{d}{d}.

$$\frac{\frac{c}{cd}-\frac{dd}{cd}}{\frac{1}{c}+6}$$

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

$$\frac{\frac{c-dd}{cd}}{\frac{1}{c}+6}$$

Do the multiplications in c-dd.

$$\frac{\frac{c-d^{2}}{cd}}{\frac{1}{c}+6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{c}{c}.

$$\frac{\frac{c-d^{2}}{cd}}{\frac{1}{c}+\frac{6c}{c}}$$

Since \frac{1}{c} and \frac{6c}{c} have the same denominator, add them by adding their numerators.

$$\frac{\frac{c-d^{2}}{cd}}{\frac{1+6c}{c}}$$

Divide \frac{c-d^{2}}{cd} by \frac{1+6c}{c} by multiplying \frac{c-d^{2}}{cd} by the reciprocal of \frac{1+6c}{c}.

$$\frac{\left(c-d^{2}\right)c}{cd\left(1+6c\right)}$$

Cancel out c in both numerator and denominator.

$$\frac{c-d^{2}}{d\left(6c+1\right)}$$

Use the distributive property to multiply d by 6c+1.

$$\frac{c-d^{2}}{6dc+d}$$