Pre-Algebra Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Combine the opposite terms in $x^{2} - 2 + 2 - x$ .

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Step 2.1

Add $- 2$ and $2$ .

$\frac{x^{2} + 0 - x}{x {(x - 1)}^{2}}$

Step 2.2

Add $x^{2}$ and $0$ .

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

Step 3

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

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Step 3.1

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

$\frac{x \cdot x - x}{x {(x - 1)}^{2}}$

Step 3.2

Factor $x$ out of $- x$ .

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

Step 3.3

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

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

Step 4

Cancel the common factor of $x$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Cancel the common factor of $x - 1$ and ${(x - 1)}^{2}$ .

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Step 5.1

Multiply by $1$ .

$\frac{(x - 1) \cdot 1}{{(x - 1)}^{2}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $x - 1$ out of ${(x - 1)}^{2}$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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