Solve 5/(w+2)^2-5/(w+2)^3

$$\frac { 5 } { ( w + 2 ) ^ { 2 } } - \frac { 5 } { ( w + 2 ) ^ { 3 } }$$

Evaluate

$$\frac{5\left(w+1\right)}{\left(w+2\right)^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(w+2\right)^{2} and \left(w+2\right)^{3} is \left(w+2\right)^{3}. Multiply \frac{5}{\left(w+2\right)^{2}} times \frac{w+2}{w+2}.

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

Since \frac{5\left(w+2\right)}{\left(w+2\right)^{3}} and \frac{5}{\left(w+2\right)^{3}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 5\left(w+2\right)-5.

$$\frac{5w+10-5}{\left(w+2\right)^{3}}$$

Combine like terms in 5w+10-5.

$$\frac{5w+5}{\left(w+2\right)^{3}}$$

Expand \left(w+2\right)^{3}.

$$\frac{5w+5}{w^{3}+6w^{2}+12w+8}$$

Expand

$$\frac{5\left(w+1\right)}{\left(w+2\right)^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(w+2\right)^{2} and \left(w+2\right)^{3} is \left(w+2\right)^{3}. Multiply \frac{5}{\left(w+2\right)^{2}} times \frac{w+2}{w+2}.

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

Since \frac{5\left(w+2\right)}{\left(w+2\right)^{3}} and \frac{5}{\left(w+2\right)^{3}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 5\left(w+2\right)-5.

$$\frac{5w+10-5}{\left(w+2\right)^{3}}$$

Combine like terms in 5w+10-5.

$$\frac{5w+5}{\left(w+2\right)^{3}}$$

Expand \left(w+2\right)^{3}.

$$\frac{5w+5}{w^{3}+6w^{2}+12w+8}$$