Solve 1/4n-1/2/frac{n{6}-1/24n}

$$\frac { \frac { 1 } { 4 n } - \frac { 1 } { 2 } } { \frac { n } { 6 } - \frac { 1 } { 24 n } }$$

Evaluate

$$-\frac{6}{2n+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4n and 2 is 4n. Multiply \frac{1}{2} times \frac{2n}{2n}.

$$\frac{\frac{1}{4n}-\frac{2n}{4n}}{\frac{n}{6}-\frac{1}{24n}}$$

Since \frac{1}{4n} and \frac{2n}{4n} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-2n}{4n}}{\frac{n}{6}-\frac{1}{24n}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 24n is 24n. Multiply \frac{n}{6} times \frac{4n}{4n}.

$$\frac{\frac{1-2n}{4n}}{\frac{n\times 4n}{24n}-\frac{1}{24n}}$$

Since \frac{n\times 4n}{24n} and \frac{1}{24n} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-2n}{4n}}{\frac{n\times 4n-1}{24n}}$$

Do the multiplications in n\times 4n-1.

$$\frac{\frac{1-2n}{4n}}{\frac{4n^{2}-1}{24n}}$$

Divide \frac{1-2n}{4n} by \frac{4n^{2}-1}{24n} by multiplying \frac{1-2n}{4n} by the reciprocal of \frac{4n^{2}-1}{24n}.

$$\frac{\left(1-2n\right)\times 24n}{4n\left(4n^{2}-1\right)}$$

Cancel out 4n in both numerator and denominator.

$$\frac{6\left(-2n+1\right)}{4n^{2}-1}$$

Factor the expressions that are not already factored.

$$\frac{6\left(-2n+1\right)}{\left(2n-1\right)\left(2n+1\right)}$$

Extract the negative sign in 1-2n.

$$\frac{-6\left(2n-1\right)}{\left(2n-1\right)\left(2n+1\right)}$$

Cancel out 2n-1 in both numerator and denominator.

$$\frac{-6}{2n+1}$$

Expand

$$-\frac{12}{4n+2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4n and 2 is 4n. Multiply \frac{1}{2} times \frac{2n}{2n}.

$$\frac{\frac{1}{4n}-\frac{2n}{4n}}{\frac{n}{6}-\frac{1}{24n}}$$

Since \frac{1}{4n} and \frac{2n}{4n} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-2n}{4n}}{\frac{n}{6}-\frac{1}{24n}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 24n is 24n. Multiply \frac{n}{6} times \frac{4n}{4n}.

$$\frac{\frac{1-2n}{4n}}{\frac{n\times 4n}{24n}-\frac{1}{24n}}$$

Since \frac{n\times 4n}{24n} and \frac{1}{24n} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-2n}{4n}}{\frac{n\times 4n-1}{24n}}$$

Do the multiplications in n\times 4n-1.

$$\frac{\frac{1-2n}{4n}}{\frac{4n^{2}-1}{24n}}$$

Divide \frac{1-2n}{4n} by \frac{4n^{2}-1}{24n} by multiplying \frac{1-2n}{4n} by the reciprocal of \frac{4n^{2}-1}{24n}.

$$\frac{\left(1-2n\right)\times 24n}{4n\left(4n^{2}-1\right)}$$

Cancel out 4n in both numerator and denominator.

$$\frac{6\left(-2n+1\right)}{4n^{2}-1}$$

Factor the expressions that are not already factored.

$$\frac{6\left(-2n+1\right)}{\left(2n-1\right)\left(2n+1\right)}$$

Extract the negative sign in 1-2n.

$$\frac{-6\left(2n-1\right)}{\left(2n-1\right)\left(2n+1\right)}$$

Cancel out 2n-1 in both numerator and denominator.

$$\frac{-6}{2n+1}$$