Solve 1-2x-2/x+3+frac{x^{2}-2x+1}{(x+3)^2}]^-1*(1-x^2-3/x):x^2-x-3/-x

$$1 - \frac { 2 x - 2 } { x + 3 } + \frac { x ^ { 2 } - 2 x + 1 } { ( x + 3 ) ^ { 2 } } ] ^ { - 1 } \cdot ( 1 - \frac { x ^ { 2 } - 3 } { x } ) : \frac { x ^ { 2 } - x - 3 } { - x }$$

Evaluate

$$\frac{16}{\left(x+3\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+3}{x+3}.

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

Since \frac{x+3}{x+3} and \frac{2x-2}{x+3} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x+3-\left(2x-2\right).

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

Combine like terms in x+3-2x+2.

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

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

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

Since \frac{\left(-x+5\right)\left(x+3\right)}{\left(x+3\right)^{2}} and \frac{x^{2}-2x+1}{\left(x+3\right)^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(-x+5\right)\left(x+3\right)+x^{2}-2x+1.

$$\frac{-x^{2}-3x+5x+15+x^{2}-2x+1}{\left(x+3\right)^{2}}$$

Combine like terms in -x^{2}-3x+5x+15+x^{2}-2x+1.

$$\frac{16}{\left(x+3\right)^{2}}$$

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

$$\frac{16}{x^{2}+6x+9}$$

Expand

$$\frac{16}{\left(x+3\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+3}{x+3}.

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

Since \frac{x+3}{x+3} and \frac{2x-2}{x+3} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x+3-\left(2x-2\right).

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

Combine like terms in x+3-2x+2.

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

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

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

Since \frac{\left(-x+5\right)\left(x+3\right)}{\left(x+3\right)^{2}} and \frac{x^{2}-2x+1}{\left(x+3\right)^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(-x+5\right)\left(x+3\right)+x^{2}-2x+1.

$$\frac{-x^{2}-3x+5x+15+x^{2}-2x+1}{\left(x+3\right)^{2}}$$

Combine like terms in -x^{2}-3x+5x+15+x^{2}-2x+1.

$$\frac{16}{\left(x+3\right)^{2}}$$

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

$$\frac{16}{x^{2}+6x+9}$$