Solve 3m^2-4n^2/mn+4n-7m/m

$$\frac { 3 m ^ { 2 } - 4 n ^ { 2 } } { m n } + \frac { 4 n - 7 m } { m }$$

Evaluate

$$\frac{3m}{n}-7$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of mn and m is mn. Multiply \frac{4n-7m}{m} times \frac{n}{n}.

$$\frac{3m^{2}-4n^{2}}{mn}+\frac{\left(4n-7m\right)n}{mn}$$

Since \frac{3m^{2}-4n^{2}}{mn} and \frac{\left(4n-7m\right)n}{mn} have the same denominator, add them by adding their numerators.

$$\frac{3m^{2}-4n^{2}+\left(4n-7m\right)n}{mn}$$

Do the multiplications in 3m^{2}-4n^{2}+\left(4n-7m\right)n.

$$\frac{3m^{2}-4n^{2}+4n^{2}-7mn}{mn}$$

Combine like terms in 3m^{2}-4n^{2}+4n^{2}-7mn.

$$\frac{3m^{2}-7mn}{mn}$$

Factor the expressions that are not already factored in \frac{3m^{2}-7mn}{mn}.

$$\frac{m\left(3m-7n\right)}{mn}$$

Cancel out m in both numerator and denominator.

$$\frac{3m-7n}{n}$$

Expand

$$\frac{3m}{n}-7$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of mn and m is mn. Multiply \frac{4n-7m}{m} times \frac{n}{n}.

$$\frac{3m^{2}-4n^{2}}{mn}+\frac{\left(4n-7m\right)n}{mn}$$

Since \frac{3m^{2}-4n^{2}}{mn} and \frac{\left(4n-7m\right)n}{mn} have the same denominator, add them by adding their numerators.

$$\frac{3m^{2}-4n^{2}+\left(4n-7m\right)n}{mn}$$

Do the multiplications in 3m^{2}-4n^{2}+\left(4n-7m\right)n.

$$\frac{3m^{2}-4n^{2}+4n^{2}-7mn}{mn}$$

Combine like terms in 3m^{2}-4n^{2}+4n^{2}-7mn.

$$\frac{3m^{2}-7mn}{mn}$$

Factor the expressions that are not already factored in \frac{3m^{2}-7mn}{mn}.

$$\frac{m\left(3m-7n\right)}{mn}$$

Cancel out m in both numerator and denominator.

$$\frac{3m-7n}{n}$$