Solve (m-3)^2/m^2-6m+9*m^3-9m/m^2-9

$$\frac { ( m - 3 ) ^ { 2 } } { m ^ { 2 } - 6 m + 9 } \cdot \frac { m ^ { 3 } - 9 m } { m ^ { 2 } - 9 }$$

Evaluate

$$m$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{\left(m-3\right)^{2}}{m^{2}-6m+9}.

$$\frac{\left(m-3\right)^{2}}{\left(m-3\right)^{2}}\times \frac{m^{3}-9m}{m^{2}-9}$$

Cancel out \left(m-3\right)^{2} in both numerator and denominator.

$$1\times \frac{m^{3}-9m}{m^{2}-9}$$

Factor the expressions that are not already factored in \frac{m^{3}-9m}{m^{2}-9}.

$$1\times \frac{m\left(m-3\right)\left(m+3\right)}{\left(m-3\right)\left(m+3\right)}$$

Cancel out \left(m-3\right)\left(m+3\right) in both numerator and denominator.

$$1m$$

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

$$m$$

Differentiate w.r.t. m

$$1$$

Steps Using Definition of a Derivative

Factor the expressions that are not already factored in \frac{\left(m-3\right)^{2}}{m^{2}-6m+9}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{\left(m-3\right)^{2}}{\left(m-3\right)^{2}}\times \frac{m^{3}-9m}{m^{2}-9})$$

Cancel out \left(m-3\right)^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}m}(1\times \frac{m^{3}-9m}{m^{2}-9})$$

Factor the expressions that are not already factored in \frac{m^{3}-9m}{m^{2}-9}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(1\times \frac{m\left(m-3\right)\left(m+3\right)}{\left(m-3\right)\left(m+3\right)})$$

Cancel out \left(m-3\right)\left(m+3\right) in both numerator and denominator.

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

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.

$$1$$