Solve 4/frac{5{m}-4/m}

$$\frac { 4 } { \frac { 5 } { m } - \frac { 4 } { m } }$$

Evaluate

$$4m$$

Solution Steps

Since \frac{5}{m} and \frac{4}{m} have the same denominator, subtract them by subtracting their numerators. Subtract 4 from 5 to get 1.

$$\frac{4}{\frac{1}{m}}$$

Divide 4 by \frac{1}{m} by multiplying 4 by the reciprocal of \frac{1}{m}.

$$4m$$

Differentiate w.r.t. m

$$4$$

Steps Using Definition of a Derivative

Since \frac{5}{m} and \frac{4}{m} have the same denominator, subtract them by subtracting their numerators. Subtract 4 from 5 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{4}{\frac{1}{m}})$$

Divide 4 by \frac{1}{m} by multiplying 4 by the reciprocal of \frac{1}{m}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(4m)$$

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

$$4m^{1-1}$$

Subtract 1 from 1.

$$4m^{0}$$

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

$$4\times 1$$

For any term t, t\times 1=t and 1t=t.

$$4$$