Solve 1+1/x-2/x^2/1-frac{3{x}+2/x^2}

$$\frac{ 1+ \frac{ 1 }{ x } - \frac{ 2 }{ { x }^{ 2 } } }{ 1- \frac{ 3 }{ x } + \frac{ 2 }{ { x }^{ 2 } } }$$

Evaluate

$$\frac{x+2}{x-2}$$

Short Solution Steps

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

$$\frac{\frac{x}{x}+\frac{1}{x}-\frac{2}{x^{2}}}{1-\frac{3}{x}+\frac{2}{x^{2}}}$$

Since \frac{x}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+1}{x}-\frac{2}{x^{2}}}{1-\frac{3}{x}+\frac{2}{x^{2}}}$$

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

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

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

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

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

$$\frac{\frac{x^{2}+x-2}{x^{2}}}{1-\frac{3}{x}+\frac{2}{x^{2}}}$$

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

$$\frac{\frac{x^{2}+x-2}{x^{2}}}{\frac{x}{x}-\frac{3}{x}+\frac{2}{x^{2}}}$$

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

$$\frac{\frac{x^{2}+x-2}{x^{2}}}{\frac{x-3}{x}+\frac{2}{x^{2}}}$$

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

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

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

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

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

$$\frac{\frac{x^{2}+x-2}{x^{2}}}{\frac{x^{2}-3x+2}{x^{2}}}$$

Divide \frac{x^{2}+x-2}{x^{2}} by \frac{x^{2}-3x+2}{x^{2}} by multiplying \frac{x^{2}+x-2}{x^{2}} by the reciprocal of \frac{x^{2}-3x+2}{x^{2}}.

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

Cancel out x^{2} in both numerator and denominator.

$$\frac{x^{2}+x-2}{x^{2}-3x+2}$$

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

$$\frac{x+2}{x-2}$$

Expand

$$\frac{x+2}{x-2}$$

Short Solution Steps

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

$$\frac{\frac{x}{x}+\frac{1}{x}-\frac{2}{x^{2}}}{1-\frac{3}{x}+\frac{2}{x^{2}}}$$

Since \frac{x}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+1}{x}-\frac{2}{x^{2}}}{1-\frac{3}{x}+\frac{2}{x^{2}}}$$

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

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

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

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

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

$$\frac{\frac{x^{2}+x-2}{x^{2}}}{1-\frac{3}{x}+\frac{2}{x^{2}}}$$

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

$$\frac{\frac{x^{2}+x-2}{x^{2}}}{\frac{x}{x}-\frac{3}{x}+\frac{2}{x^{2}}}$$

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

$$\frac{\frac{x^{2}+x-2}{x^{2}}}{\frac{x-3}{x}+\frac{2}{x^{2}}}$$

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

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

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

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

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

$$\frac{\frac{x^{2}+x-2}{x^{2}}}{\frac{x^{2}-3x+2}{x^{2}}}$$

Divide \frac{x^{2}+x-2}{x^{2}} by \frac{x^{2}-3x+2}{x^{2}} by multiplying \frac{x^{2}+x-2}{x^{2}} by the reciprocal of \frac{x^{2}-3x+2}{x^{2}}.

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

Cancel out x^{2} in both numerator and denominator.

$$\frac{x^{2}+x-2}{x^{2}-3x+2}$$

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

$$\frac{x+2}{x-2}$$