Solve a/b+1-a/(b+1)^2

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in ab+a-a.

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

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

$$\frac{ab}{b^{2}+2b+1}$$

Expand

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in ab+a-a.

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

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

$$\frac{ab}{b^{2}+2b+1}$$