Solve 1/1+2-4/(2+x)^2

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

Evaluate

$$\frac{x^{2}+4x-8}{3\left(x+2\right)^{2}}$$

Short Solution Steps

Add 1 and 2 to get 3.

$$\frac{1}{3}-\frac{4}{\left(2+x\right)^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and \left(2+x\right)^{2} is 3\left(x+2\right)^{2}. Multiply \frac{1}{3} times \frac{\left(x+2\right)^{2}}{\left(x+2\right)^{2}}. Multiply \frac{4}{\left(2+x\right)^{2}} times \frac{3}{3}.

$$\frac{\left(x+2\right)^{2}}{3\left(x+2\right)^{2}}-\frac{4\times 3}{3\left(x+2\right)^{2}}$$

Since \frac{\left(x+2\right)^{2}}{3\left(x+2\right)^{2}} and \frac{4\times 3}{3\left(x+2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x+2\right)^{2}-4\times 3}{3\left(x+2\right)^{2}}$$

Do the multiplications in \left(x+2\right)^{2}-4\times 3.

$$\frac{x^{2}+4x+4-12}{3\left(x+2\right)^{2}}$$

Combine like terms in x^{2}+4x+4-12.

$$\frac{x^{2}+4x-8}{3\left(x+2\right)^{2}}$$

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

$$\frac{x^{2}+4x-8}{3x^{2}+12x+12}$$

Expand

$$\frac{x^{2}+4x-8}{3\left(x+2\right)^{2}}$$

Short Solution Steps

Add 1 and 2 to get 3.

$$\frac{1}{3}-\frac{4}{\left(2+x\right)^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and \left(2+x\right)^{2} is 3\left(x+2\right)^{2}. Multiply \frac{1}{3} times \frac{\left(x+2\right)^{2}}{\left(x+2\right)^{2}}. Multiply \frac{4}{\left(2+x\right)^{2}} times \frac{3}{3}.

$$\frac{\left(x+2\right)^{2}}{3\left(x+2\right)^{2}}-\frac{4\times 3}{3\left(x+2\right)^{2}}$$

Since \frac{\left(x+2\right)^{2}}{3\left(x+2\right)^{2}} and \frac{4\times 3}{3\left(x+2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x+2\right)^{2}-4\times 3}{3\left(x+2\right)^{2}}$$

Do the multiplications in \left(x+2\right)^{2}-4\times 3.

$$\frac{x^{2}+4x+4-12}{3\left(x+2\right)^{2}}$$

Combine like terms in x^{2}+4x+4-12.

$$\frac{x^{2}+4x-8}{3\left(x+2\right)^{2}}$$

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

$$\frac{x^{2}+4x-8}{3x^{2}+12x+12}$$