Solve 2/x+x/m/frac{m{x}-3/m}

$$\frac { \frac { 2 } { x } + \frac { x } { m } } { \frac { m } { x } - \frac { 3 } { m } }$$

Evaluate

$$\frac{x^{2}+2m}{m^{2}-3x}$$

Short Solution Steps

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

$$\frac{\frac{2m}{mx}+\frac{xx}{mx}}{\frac{m}{x}-\frac{3}{m}}$$

Since \frac{2m}{mx} and \frac{xx}{mx} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2m+xx}{mx}}{\frac{m}{x}-\frac{3}{m}}$$

Do the multiplications in 2m+xx.

$$\frac{\frac{2m+x^{2}}{mx}}{\frac{m}{x}-\frac{3}{m}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and m is mx. Multiply \frac{m}{x} times \frac{m}{m}. Multiply \frac{3}{m} times \frac{x}{x}.

$$\frac{\frac{2m+x^{2}}{mx}}{\frac{mm}{mx}-\frac{3x}{mx}}$$

Since \frac{mm}{mx} and \frac{3x}{mx} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2m+x^{2}}{mx}}{\frac{mm-3x}{mx}}$$

Do the multiplications in mm-3x.

$$\frac{\frac{2m+x^{2}}{mx}}{\frac{m^{2}-3x}{mx}}$$

Divide \frac{2m+x^{2}}{mx} by \frac{m^{2}-3x}{mx} by multiplying \frac{2m+x^{2}}{mx} by the reciprocal of \frac{m^{2}-3x}{mx}.

$$\frac{\left(2m+x^{2}\right)mx}{mx\left(m^{2}-3x\right)}$$

Cancel out mx in both numerator and denominator.

$$\frac{x^{2}+2m}{-3x+m^{2}}$$

Expand

$$\frac{x^{2}+2m}{m^{2}-3x}$$

Short Solution Steps

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

$$\frac{\frac{2m}{mx}+\frac{xx}{mx}}{\frac{m}{x}-\frac{3}{m}}$$

Since \frac{2m}{mx} and \frac{xx}{mx} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2m+xx}{mx}}{\frac{m}{x}-\frac{3}{m}}$$

Do the multiplications in 2m+xx.

$$\frac{\frac{2m+x^{2}}{mx}}{\frac{m}{x}-\frac{3}{m}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and m is mx. Multiply \frac{m}{x} times \frac{m}{m}. Multiply \frac{3}{m} times \frac{x}{x}.

$$\frac{\frac{2m+x^{2}}{mx}}{\frac{mm}{mx}-\frac{3x}{mx}}$$

Since \frac{mm}{mx} and \frac{3x}{mx} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2m+x^{2}}{mx}}{\frac{mm-3x}{mx}}$$

Do the multiplications in mm-3x.

$$\frac{\frac{2m+x^{2}}{mx}}{\frac{m^{2}-3x}{mx}}$$

Divide \frac{2m+x^{2}}{mx} by \frac{m^{2}-3x}{mx} by multiplying \frac{2m+x^{2}}{mx} by the reciprocal of \frac{m^{2}-3x}{mx}.

$$\frac{\left(2m+x^{2}\right)mx}{mx\left(m^{2}-3x\right)}$$

Cancel out mx in both numerator and denominator.

$$\frac{x^{2}+2m}{-3x+m^{2}}$$