Solve m^2-7m+18/m^2+1

$$m ^ { 2 } - 7 m + \frac { 18 } { m ^ { 2 } + 1 }$$

Evaluate

$$\frac{m^{4}-7m^{3}+m^{2}-7m+18}{m^{2}+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply m^{2}-7m times \frac{m^{2}+1}{m^{2}+1}.

$$\frac{\left(m^{2}-7m\right)\left(m^{2}+1\right)}{m^{2}+1}+\frac{18}{m^{2}+1}$$

Since \frac{\left(m^{2}-7m\right)\left(m^{2}+1\right)}{m^{2}+1} and \frac{18}{m^{2}+1} have the same denominator, add them by adding their numerators.

$$\frac{\left(m^{2}-7m\right)\left(m^{2}+1\right)+18}{m^{2}+1}$$

Do the multiplications in \left(m^{2}-7m\right)\left(m^{2}+1\right)+18.

$$\frac{m^{4}+m^{2}-7m^{3}-7m+18}{m^{2}+1}$$

Differentiate w.r.t. m

$$\frac{\left(m+1\right)\left(2m^{4}-9m^{3}+13m^{2}-27m-7\right)}{\left(m^{2}+1\right)^{2}}$$