Solve 4/m^2n+6/mn^2/frac{12{m^2n}-1/mn^2}

$$\frac { \frac { 4 } { m ^ { 2 } n } + \frac { 6 } { m n ^ { 2 } } } { \frac { 12 } { m ^ { 2 } n } - \frac { 1 } { m n ^ { 2 } } }$$

Evaluate

$$\frac{2\left(3m+2n\right)}{12n-m}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m^{2}n and mn^{2} is m^{2}n^{2}. Multiply \frac{4}{m^{2}n} times \frac{n}{n}. Multiply \frac{6}{mn^{2}} times \frac{m}{m}.

$$\frac{\frac{4n}{m^{2}n^{2}}+\frac{6m}{m^{2}n^{2}}}{\frac{12}{m^{2}n}-\frac{1}{mn^{2}}}$$

Since \frac{4n}{m^{2}n^{2}} and \frac{6m}{m^{2}n^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4n+6m}{m^{2}n^{2}}}{\frac{12}{m^{2}n}-\frac{1}{mn^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m^{2}n and mn^{2} is m^{2}n^{2}. Multiply \frac{12}{m^{2}n} times \frac{n}{n}. Multiply \frac{1}{mn^{2}} times \frac{m}{m}.

$$\frac{\frac{4n+6m}{m^{2}n^{2}}}{\frac{12n}{m^{2}n^{2}}-\frac{m}{m^{2}n^{2}}}$$

Since \frac{12n}{m^{2}n^{2}} and \frac{m}{m^{2}n^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4n+6m}{m^{2}n^{2}}}{\frac{12n-m}{m^{2}n^{2}}}$$

Divide \frac{4n+6m}{m^{2}n^{2}} by \frac{12n-m}{m^{2}n^{2}} by multiplying \frac{4n+6m}{m^{2}n^{2}} by the reciprocal of \frac{12n-m}{m^{2}n^{2}}.

$$\frac{\left(4n+6m\right)m^{2}n^{2}}{m^{2}n^{2}\left(12n-m\right)}$$

Cancel out m^{2}n^{2} in both numerator and denominator.

$$\frac{6m+4n}{-m+12n}$$

Expand

$$\frac{2\left(3m+2n\right)}{12n-m}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m^{2}n and mn^{2} is m^{2}n^{2}. Multiply \frac{4}{m^{2}n} times \frac{n}{n}. Multiply \frac{6}{mn^{2}} times \frac{m}{m}.

$$\frac{\frac{4n}{m^{2}n^{2}}+\frac{6m}{m^{2}n^{2}}}{\frac{12}{m^{2}n}-\frac{1}{mn^{2}}}$$

Since \frac{4n}{m^{2}n^{2}} and \frac{6m}{m^{2}n^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4n+6m}{m^{2}n^{2}}}{\frac{12}{m^{2}n}-\frac{1}{mn^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m^{2}n and mn^{2} is m^{2}n^{2}. Multiply \frac{12}{m^{2}n} times \frac{n}{n}. Multiply \frac{1}{mn^{2}} times \frac{m}{m}.

$$\frac{\frac{4n+6m}{m^{2}n^{2}}}{\frac{12n}{m^{2}n^{2}}-\frac{m}{m^{2}n^{2}}}$$

Since \frac{12n}{m^{2}n^{2}} and \frac{m}{m^{2}n^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4n+6m}{m^{2}n^{2}}}{\frac{12n-m}{m^{2}n^{2}}}$$

Divide \frac{4n+6m}{m^{2}n^{2}} by \frac{12n-m}{m^{2}n^{2}} by multiplying \frac{4n+6m}{m^{2}n^{2}} by the reciprocal of \frac{12n-m}{m^{2}n^{2}}.

$$\frac{\left(4n+6m\right)m^{2}n^{2}}{m^{2}n^{2}\left(12n-m\right)}$$

Cancel out m^{2}n^{2} in both numerator and denominator.

$$\frac{6m+4n}{-m+12n}$$