Algebra Examples

$\frac{4 x}{x + 2} = x$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x + 2, 1$

Step 1.2

Remove parentheses.

$x + 2, 1$

Step 1.3

The LCM of one and any expression is the expression.

$x + 2$

Step 2

Multiply each term in $\frac{4 x}{x + 2} = x$ by $x + 2$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{4 x}{x + 2} = x$ by $x + 2$ .

$\frac{4 x}{x + 2} (x + 2) = x (x + 2)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $x + 2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 x}{x + 2} (x + 2) = x (x + 2)$

Step 2.2.1.2

Rewrite the expression.

$4 x = x (x + 2)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

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

Step 2.3.2

Simplify the expression.

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Step 2.3.2.1

Multiply $x$ by $x$ .

$4 x = x^{2} + x \cdot 2$

Step 2.3.2.2

Move $2$ to the left of $x$ .

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

Step 3

Solve the equation.

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Step 3.1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Step 3.2

Move all terms containing $x$ to the left side of the equation.

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Step 3.2.1

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

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

Step 3.2.2

Subtract $4 x$ from $2 x$ .

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

Step 3.3

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

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Step 3.3.1

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

$x \cdot x - 2 x = 0$

Step 3.3.2

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

$x \cdot x + x \cdot - 2 = 0$

Step 3.3.3

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

$x (x - 2) = 0$

Step 3.4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 2 = 0$

Step 3.5

Set $x$ equal to $0$ .

$x = 0$

Step 3.6

Set $x - 2$ equal to $0$ and solve for $x$ .

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Step 3.6.1

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

$x - 2 = 0$

Step 3.6.2

Add $2$ to both sides of the equation.

$x = 2$

Step 3.7

The final solution is all the values that make $x (x - 2) = 0$ true.

$x = 0, 2$