Solve -1/4left(x+2right)^4+2/5left(x+2right)^5

$$\frac{ -1 }{ 4 { \left(x+2 \right) }^{ 4 } } + \frac{ 2 }{ 5 { \left(x+2 \right) }^{ 5 } }$$

Evaluate

$$-\frac{5x+2}{20\left(x+2\right)^{5}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(x+2\right)^{4} and 5\left(x+2\right)^{5} is 20\left(x+2\right)^{5}. Multiply \frac{-1}{4\left(x+2\right)^{4}} times \frac{5\left(x+2\right)}{5\left(x+2\right)}. Multiply \frac{2}{5\left(x+2\right)^{5}} times \frac{4}{4}.

$$\frac{-5\left(x+2\right)}{20\left(x+2\right)^{5}}+\frac{2\times 4}{20\left(x+2\right)^{5}}$$

Since \frac{-5\left(x+2\right)}{20\left(x+2\right)^{5}} and \frac{2\times 4}{20\left(x+2\right)^{5}} have the same denominator, add them by adding their numerators.

$$\frac{-5\left(x+2\right)+2\times 4}{20\left(x+2\right)^{5}}$$

Do the multiplications in -5\left(x+2\right)+2\times 4.

$$\frac{-5x-10+8}{20\left(x+2\right)^{5}}$$

Combine like terms in -5x-10+8.

$$\frac{-5x-2}{20\left(x+2\right)^{5}}$$

Expand 20\left(x+2\right)^{5}.

$$\frac{-5x-2}{20x^{5}+200x^{4}+800x^{3}+1600x^{2}+1600x+640}$$

Expand

$$-\frac{5x+2}{20\left(x+2\right)^{5}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(x+2\right)^{4} and 5\left(x+2\right)^{5} is 20\left(x+2\right)^{5}. Multiply \frac{-1}{4\left(x+2\right)^{4}} times \frac{5\left(x+2\right)}{5\left(x+2\right)}. Multiply \frac{2}{5\left(x+2\right)^{5}} times \frac{4}{4}.

$$\frac{-5\left(x+2\right)}{20\left(x+2\right)^{5}}+\frac{2\times 4}{20\left(x+2\right)^{5}}$$

Since \frac{-5\left(x+2\right)}{20\left(x+2\right)^{5}} and \frac{2\times 4}{20\left(x+2\right)^{5}} have the same denominator, add them by adding their numerators.

$$\frac{-5\left(x+2\right)+2\times 4}{20\left(x+2\right)^{5}}$$

Do the multiplications in -5\left(x+2\right)+2\times 4.

$$\frac{-5x-10+8}{20\left(x+2\right)^{5}}$$

Combine like terms in -5x-10+8.

$$\frac{-5x-2}{20\left(x+2\right)^{5}}$$

Expand 20\left(x+2\right)^{5}.

$$\frac{-5x-2}{20x^{5}+200x^{4}+800x^{3}+1600x^{2}+1600x+640}$$