Solve (1-1/m+1)*(m+1)

$$( 1 - \frac { 1 } { m + 1 } ) \cdot ( m + 1 )$$

Evaluate

$$m$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{m+1}{m+1}.

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

Since \frac{m+1}{m+1} and \frac{1}{m+1} have the same denominator, subtract them by subtracting their numerators.

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

Combine like terms in m+1-1.

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

Cancel out m+1 and m+1.

$$m$$

Differentiate w.r.t. m

$$1$$

Steps Using Definition of a Derivative

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{m+1}{m+1}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(\frac{m+1}{m+1}-\frac{1}{m+1}\right)\left(m+1\right))$$

Since \frac{m+1}{m+1} and \frac{1}{m+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m+1-1}{m+1}\left(m+1\right))$$

Combine like terms in m+1-1.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m}{m+1}\left(m+1\right))$$

Cancel out m+1 and m+1.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m)$$

The derivative of ax^{n} is nax^{n-1}.

$$m^{1-1}$$

Subtract 1 from 1.

$$m^{0}$$

For any term t except 0, t^{0}=1.

$$1$$