Solve b^2-7b+5+3/b+2

$$b ^ { 2 } - 7 b + 5 + \frac { 3 } { b + 2 }$$

Evaluate

$$\frac{\left(b-1\right)\left(b^{2}-4b-13\right)}{b+2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply b^{2}-7b+5 times \frac{b+2}{b+2}.

$$\frac{\left(b^{2}-7b+5\right)\left(b+2\right)}{b+2}+\frac{3}{b+2}$$

Since \frac{\left(b^{2}-7b+5\right)\left(b+2\right)}{b+2} and \frac{3}{b+2} have the same denominator, add them by adding their numerators.

$$\frac{\left(b^{2}-7b+5\right)\left(b+2\right)+3}{b+2}$$

Do the multiplications in \left(b^{2}-7b+5\right)\left(b+2\right)+3.

$$\frac{b^{3}+2b^{2}-7b^{2}-14b+5b+10+3}{b+2}$$

Combine like terms in b^{3}+2b^{2}-7b^{2}-14b+5b+10+3.

$$\frac{b^{3}-5b^{2}-9b+13}{b+2}$$

Differentiate w.r.t. b

$$\frac{2b^{3}+b^{2}-20b-31}{\left(b+2\right)^{2}}$$