Solve for x x^2=(3x)/(x-2)

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

Step 1

Find the LCD of the terms in the equation.

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

$1, x - 2$

Remove parentheses.

$1, x - 2$

The LCM of one and any expression is the expression.

$x - 2$

Step 2

Multiply each term in $x^{2} = \frac{3 x}{x - 2}$ by $x - 2$ to eliminate the fractions.

Multiply each term in $x^{2} = \frac{3 x}{x - 2}$ by $x - 2$ .

$x^{2} (x - 2) = \frac{3 x}{x - 2} (x - 2)$

Simplify the left side.

Apply the distributive property.

$x^{2} x + x^{2} \cdot - 2 = \frac{3 x}{x - 2} (x - 2)$

Multiply $x^{2}$ by $x$ by adding the exponents.

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$x^{2} x^{1} + x^{2} \cdot - 2 = \frac{3 x}{x - 2} (x - 2)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2 + 1} + x^{2} \cdot - 2 = \frac{3 x}{x - 2} (x - 2)$

Add $2$ and $1$ .

$x^{3} + x^{2} \cdot - 2 = \frac{3 x}{x - 2} (x - 2)$

Move $- 2$ to the left of $x^{2}$ .

$x^{3} - 2 x^{2} = \frac{3 x}{x - 2} (x - 2)$

Simplify the right side.

Cancel the common factor of $x - 2$ .

Cancel the common factor.

$x^{3} - 2 x^{2} = \frac{3 x}{x - 2} (x - 2)$

Rewrite the expression.

$x^{3} - 2 x^{2} = 3 x$

Step 3

Solve the equation.

Subtract $3 x$ from both sides of the equation.

$x^{3} - 2 x^{2} - 3 x = 0$

Factor the left side of the equation.

Factor $x$ out of $x^{3} - 2 x^{2} - 3 x$ .

Factor $x$ out of $x^{3}$ .

$x \cdot x^{2} - 2 x^{2} - 3 x = 0$

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

$x \cdot x^{2} + x (- 2 x) - 3 x = 0$

Factor $x$ out of $- 3 x$ .

$x \cdot x^{2} + x (- 2 x) + x \cdot - 3 = 0$

Factor $x$ out of $x \cdot x^{2} + x (- 2 x)$ .

$x (x^{2} - 2 x) + x \cdot - 3 = 0$

Factor $x$ out of $x (x^{2} - 2 x) + x \cdot - 3$ .

$x (x^{2} - 2 x - 3) = 0$

Factor.

Factor $x^{2} - 2 x - 3$ using the AC method.

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 $- 3$ and whose sum is $- 2$ .

$- 3, 1$

Write the factored form using these integers.

$x ((x - 3) (x + 1)) = 0$

Remove unnecessary parentheses.

$x (x - 3) (x + 1) = 0$

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

$x = 0$

$x - 3 = 0$

$x + 1 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 3$ equal to $0$ and solve for $x$ .

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

The final solution is all the values that make $x (x - 3) (x + 1) = 0$ true.

$x = 0, 3, - 1$

Solve for x x^2=(3x)/(x-2)

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