Solve 1/x+x/x+1-1/x^2+x=

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

Evaluate

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Short Solution Steps

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

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

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

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

Do the multiplications in x+1+xx.

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

Factor x^{2}+x.

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

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

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

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

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

Factor the expressions that are not already factored in \frac{x+x^{2}}{x\left(x+1\right)}.

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

Cancel out x\left(x+1\right) in both numerator and denominator.

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Factor

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