Solve for x 1-(3x)/(x-8)=x

$1 - \frac{3 x}{x - 8} = x$

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.

$1, x - 8, 1$

Remove parentheses.

$1, x - 8, 1$

The LCM of one and any expression is the expression.

$x - 8$

Multiply each term in $1 - \frac{3 x}{x - 8} = x$ by $x - 8$ to eliminate the fractions.

Multiply each term in $1 - \frac{3 x}{x - 8} = x$ by $x - 8$ .

$1 (x - 8) - \frac{3 x}{x - 8} (x - 8) = x (x - 8)$

Simplify the left side.

Simplify each term.

Multiply $x - 8$ by $1$ .

$x - 8 - \frac{3 x}{x - 8} (x - 8) = x (x - 8)$

Cancel the common factor of $x - 8$ .

Move the leading negative in $- \frac{3 x}{x - 8}$ into the numerator.

$x - 8 + \frac{- 3 x}{x - 8} (x - 8) = x (x - 8)$

Cancel the common factor.

$x - 8 + \frac{- 3 x}{x - 8} (x - 8) = x (x - 8)$

Rewrite the expression.

$x - 8 - 3 x = x (x - 8)$

Subtract $3 x$ from $x$ .

$- 2 x - 8 = x (x - 8)$

Simplify the right side.

Apply the distributive property.

$- 2 x - 8 = x \cdot x + x \cdot - 8$

Simplify the expression.

Multiply $x$ by $x$ .

$- 2 x - 8 = x^{2} + x \cdot - 8$

Move $- 8$ to the left of $x$ .

$- 2 x - 8 = x^{2} - 8 x$

Solve the equation.

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

$x^{2} - 8 x = - 2 x - 8$

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

Add $2 x$ to both sides of the equation.

$x^{2} - 8 x + 2 x = - 8$

Add $- 8 x$ and $2 x$ .

$x^{2} - 6 x = - 8$

Add $8$ to both sides of the equation.

$x^{2} - 6 x + 8 = 0$

Factor $x^{2} - 6 x + 8$ 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 $8$ and whose sum is $- 6$ .

$- 4, - 2$

Write the factored form using these integers.

$(x - 4) (x - 2) = 0$

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

$x - 4 = 0$

$x - 2 = 0$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

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

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

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

The final solution is all the values that make $(x - 4) (x - 2) = 0$ true.

$x = 4, 2$

Solve for x 1-(3x)/(x-8)=x

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