Algebra Examples

$\frac{x^{2} - 5 x + 4}{x^{2}} \div \frac{x - 1}{x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - 5 x + 4}{x^{2}} \cdot \frac{x}{x - 1}$

Step 2

Cancel the common factor of $x$ .

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Step 2.1

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

$\frac{x^{2} - 5 x + 4}{x \cdot x} \cdot \frac{x}{x - 1}$

Step 2.2

Cancel the common factor.

$\frac{x^{2} - 5 x + 4}{x \cdot x} \cdot \frac{x}{x - 1}$

Step 2.3

Rewrite the expression.

$\frac{x^{2} - 5 x + 4}{x} \cdot \frac{1}{x - 1}$

Step 3

Multiply $\frac{x^{2} - 5 x + 4}{x}$ by $\frac{1}{x - 1}$ .

$\frac{x^{2} - 5 x + 4}{x (x - 1)}$

Step 4

Factor $x^{2} - 5 x + 4$ using the AC method.

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Step 4.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $4$ and whose sum is $- 5$ .

$- 4, - 1$

Step 4.2

Write the factored form using these integers.

$\frac{(x - 4) (x - 1)}{x (x - 1)}$

Step 5

Cancel the common factor of $x - 1$ .

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Step 5.1

Cancel the common factor.

$\frac{(x - 4) (x - 1)}{x (x - 1)}$

Step 5.2

Rewrite the expression.

$\frac{x - 4}{x}$

Step 6

Split the fraction $\frac{x - 4}{x}$ into two fractions.

$\frac{x}{x} + \frac{- 4}{x}$

Step 7

Cancel the common factor of $x$ .

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Step 7.1

Cancel the common factor.

$\frac{x}{x} + \frac{- 4}{x}$

Step 7.2

Rewrite the expression.

$1 + \frac{- 4}{x}$

Step 8

Move the negative in front of the fraction.

$1 - \frac{4}{x}$