Solve x+1/(x+2)^2-1/x+2

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

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in x+1-\left(x+2\right).

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

Combine like terms in x+1-x-2.

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

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

$$\frac{-1}{x^{2}+4x+4}$$

Expand

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

Short Solution Steps

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

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

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

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

Do the multiplications in x+1-\left(x+2\right).

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

Combine like terms in x+1-x-2.

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

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

$$\frac{-1}{x^{2}+4x+4}$$