Solve b/a^2+2a+1-b^2/ab+b

$$\frac { b } { a ^ { 2 } + 2 a + 1 } - \frac { b ^ { 2 } } { a b + b }$$

Evaluate

$$-\frac{ab}{\left(a+1\right)^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{b^{2}}{ab+b}.

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

Cancel out b in both numerator and denominator.

$$\frac{b}{a^{2}+2a+1}-\frac{b}{a+1}$$

Factor a^{2}+2a+1.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(a+1\right)^{2} and a+1 is \left(a+1\right)^{2}. Multiply \frac{b}{a+1} times \frac{a+1}{a+1}.

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

Since \frac{b}{\left(a+1\right)^{2}} and \frac{b\left(a+1\right)}{\left(a+1\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in b-b\left(a+1\right).

$$\frac{b-ba-b}{\left(a+1\right)^{2}}$$

Combine like terms in b-ba-b.

$$\frac{-ba}{\left(a+1\right)^{2}}$$

Expand \left(a+1\right)^{2}.

$$\frac{-ba}{a^{2}+2a+1}$$

Factor

$$-\frac{ab}{\left(a+1\right)^{2}}$$