Solve a^2/a+1-a^3/a^2+2a+1

$$\frac { a ^ { 2 } } { a + 1 } - \frac { a ^ { 3 } } { a ^ { 2 } + 2 a + 1 }$$

Evaluate

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

Short Solution Steps

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

$$\frac{a^{2}}{a+1}-\frac{a^{3}}{\left(a+1\right)^{2}}$$

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

$$\frac{a^{2}\left(a+1\right)}{\left(a+1\right)^{2}}-\frac{a^{3}}{\left(a+1\right)^{2}}$$

Since \frac{a^{2}\left(a+1\right)}{\left(a+1\right)^{2}} and \frac{a^{3}}{\left(a+1\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{a^{2}\left(a+1\right)-a^{3}}{\left(a+1\right)^{2}}$$

Do the multiplications in a^{2}\left(a+1\right)-a^{3}.

$$\frac{a^{3}+a^{2}-a^{3}}{\left(a+1\right)^{2}}$$

Combine like terms in a^{3}+a^{2}-a^{3}.

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

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

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

Factor

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