Algebra Examples

$\frac{x^{2} - 4 x}{x - 1} \cdot \frac{x^{2} + 3 x - 4}{2 x}$

Step 1

Set the denominator in $\frac{x^{2} - 4 x}{x - 1}$ equal to $0$ to find where the expression is undefined.

$x - 1 = 0$

Step 2

Add $1$ to both sides of the equation.

$x = 1$

Step 3

Set the denominator in $\frac{x^{2} + 3 x - 4}{2 x}$ equal to $0$ to find where the expression is undefined.

$2 x = 0$

Step 4

Divide each term in $2 x = 0$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 x = 0$ by $2$ .

$\frac{2 x}{2} = \frac{0}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{0}{2}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $2$ .

$x = 0$

Step 5

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x = 0, x = 1$

Step 6