Algebra Examples

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

Step 1

Factor each term.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

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

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

Step 1.1.3

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

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

Step 1.1.4

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

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

Step 1.2

Reduce the expression by cancelling the common factors.

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Step 1.2.1

Reduce the expression $\frac{x (x + 1)}{x}$ by cancelling the common factors.

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Step 1.2.1.1

Cancel the common factor.

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

Step 1.2.1.2

Rewrite the expression.

$\frac{x + 1}{1} = x + 1$

Step 1.2.2

Divide $x + 1$ by $1$ .

$x + 1 = x + 1$

Step 2

Solve the equation.

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Step 2.1

Move all terms containing $x$ to the left side of the equation.

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Step 2.1.1

Subtract $x$ from both sides of the equation.

$x + 1 - x = 1$

Step 2.1.2

Combine the opposite terms in $x + 1 - x$ .

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Step 2.1.2.1

Subtract $x$ from $x$ .

$0 + 1 = 1$

Step 2.1.2.2

Add $0$ and $1$ .

$1 = 1$

Step 2.2

Since $1 = 1$ , the equation will always be true for any value of $x$ .

All real numbers

Step 3

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$