Solve +(m/m+1)+g(1/m)

$$+ ( \frac { m } { m + 1 } ) + g ( \frac { 1 } { m } )$$

Evaluate

$$\frac{m^{2}+gm+g}{m\left(m+1\right)}$$

Short Solution Steps

Express g\times \frac{1}{m} as a single fraction.

$$\frac{m}{m+1}+\frac{g}{m}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m+1 and m is m\left(m+1\right). Multiply \frac{m}{m+1} times \frac{m}{m}. Multiply \frac{g}{m} times \frac{m+1}{m+1}.

$$\frac{mm}{m\left(m+1\right)}+\frac{g\left(m+1\right)}{m\left(m+1\right)}$$

Since \frac{mm}{m\left(m+1\right)} and \frac{g\left(m+1\right)}{m\left(m+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{mm+g\left(m+1\right)}{m\left(m+1\right)}$$

Do the multiplications in mm+g\left(m+1\right).

$$\frac{m^{2}+gm+g}{m\left(m+1\right)}$$

Expand m\left(m+1\right).

$$\frac{m^{2}+gm+g}{m^{2}+m}$$

Factor

$$\frac{m^{2}+gm+g}{m\left(m+1\right)}$$