Algebra Examples

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

Step 1

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$x \cdot x = (x - 1) \cdot 4$

Step 2

Solve the equation for $x$ .

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Step 2.1

Simplify $x \cdot x$ .

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Step 2.1.1

Rewrite.

$0 + 0 + x \cdot x = (x - 1) \cdot 4$

Step 2.1.2

Simplify by adding zeros.

$x \cdot x = (x - 1) \cdot 4$

Step 2.1.3

Multiply $x$ by $x$ .

$x^{2} = (x - 1) \cdot 4$

Step 2.2

Simplify $(x - 1) \cdot 4$ .

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Step 2.2.1

Apply the distributive property.

$x^{2} = x \cdot 4 - 1 \cdot 4$

Step 2.2.2

Simplify the expression.

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Step 2.2.2.1

Move $4$ to the left of $x$ .

$x^{2} = 4 \cdot x - 1 \cdot 4$

Step 2.2.2.2

Multiply $- 1$ by $4$ .

$x^{2} = 4 x - 4$

Step 2.3

Subtract $4 x$ from both sides of the equation.

$x^{2} - 4 x = - 4$

Step 2.4

Add $4$ to both sides of the equation.

$x^{2} - 4 x + 4 = 0$

Step 2.5

Factor using the perfect square rule.

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Step 2.5.1

Rewrite $4$ as $2^{2}$ .

$x^{2} - 4 x + 2^{2} = 0$

Step 2.5.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 x = 2 \cdot x \cdot 2$

Step 2.5.3

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 2 + 2^{2} = 0$

Step 2.5.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 2$ .

${(x - 2)}^{2} = 0$

Step 2.6

Set the $x - 2$ equal to $0$ .

$x - 2 = 0$

Step 2.7

Add $2$ to both sides of the equation.

$x = 2$