Calculus Examples

$\frac{lim_{x \to 0} 1}{x} - \frac{1}{x^{2} + x}$

Step 1

Evaluate the limit of $1$ which is constant as $x$ approaches $0$ .

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

Step 2

Factor $x$ out of $x^{2} + x$ .

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Step 2.1

Factor $x$ out of $x^{2}$ .

$\frac{1}{x} - \frac{1}{x \cdot x + x}$

Step 2.2

Raise $x$ to the power of $1$ .

$\frac{1}{x} - \frac{1}{x \cdot x + x^{1}}$

Step 2.3

Factor $x$ out of $x^{1}$ .

$\frac{1}{x} - \frac{1}{x \cdot x + x \cdot 1}$

Step 2.4

Factor $x$ out of $x \cdot x + x \cdot 1$ .

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