Pre-Algebra Examples

$\frac{4 x - 3}{x^{2} - 2 x} + \frac{- 3 x + 3}{x^{2} - 2 x}$

Step 1

Combine the numerators over the common denominator.

$\frac{4 x - 3 - 3 x + 3}{x^{2} - 2 x}$

Step 2

Combine the opposite terms in $4 x - 3 - 3 x + 3$ .

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Step 2.1

Add $- 3$ and $3$ .

$\frac{4 x - 3 x + 0}{x^{2} - 2 x}$

Step 2.2

Add $4 x - 3 x$ and $0$ .

$\frac{4 x - 3 x}{x^{2} - 2 x}$

Step 3

Subtract $3 x$ from $4 x$ .

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Factor $x$ out of $- 2 x$ .

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

Step 4.3

Factor $x$ out of $x \cdot x + x \cdot - 2$ .

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

Step 5

Cancel the common factor of $x$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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