Solve for x x+(3x)/(x-10)=2

$x + \frac{3 x}{x - 10} = 2$

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.

$1, x - 10, 1$

Remove parentheses.

$1, x - 10, 1$

The LCM of one and any expression is the expression.

$x - 10$

Multiply each term in $x + \frac{3 x}{x - 10} = 2$ by $x - 10$ to eliminate the fractions.

Multiply each term in $x + \frac{3 x}{x - 10} = 2$ by $x - 10$ .

$x (x - 10) + \frac{3 x}{x - 10} (x - 10) = 2 (x - 10)$

Simplify the left side.

Simplify each term.

Apply the distributive property.

$x \cdot x + x \cdot - 10 + \frac{3 x}{x - 10} (x - 10) = 2 (x - 10)$

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 10 + \frac{3 x}{x - 10} (x - 10) = 2 (x - 10)$

Move $- 10$ to the left of $x$ .

$x^{2} - 10 \cdot x + \frac{3 x}{x - 10} (x - 10) = 2 (x - 10)$

Cancel the common factor of $x - 10$ .

Cancel the common factor.

$x^{2} - 10 x + \frac{3 x}{x - 10} (x - 10) = 2 (x - 10)$

Rewrite the expression.

$x^{2} - 10 x + 3 x = 2 (x - 10)$

Add $- 10 x$ and $3 x$ .

$x^{2} - 7 x = 2 (x - 10)$

Simplify the right side.

Apply the distributive property.

$x^{2} - 7 x = 2 x + 2 \cdot - 10$

Multiply $2$ by $- 10$ .

$x^{2} - 7 x = 2 x - 20$

Solve the equation.

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

Subtract $2 x$ from both sides of the equation.

$x^{2} - 7 x - 2 x = - 20$

Subtract $2 x$ from $- 7 x$ .

$x^{2} - 9 x = - 20$

Add $20$ to both sides of the equation.

$x^{2} - 9 x + 20 = 0$

Factor $x^{2} - 9 x + 20$ 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 $20$ and whose sum is $- 9$ .

$- 5, - 4$

Write the factored form using these integers.

$(x - 5) (x - 4) = 0$

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

$x - 5 = 0$

$x - 4 = 0$

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

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.

$x = 4$

The final solution is all the values that make $(x - 5) (x - 4) = 0$ true.

$x = 5, 4$

Solve for x x+(3x)/(x-10)=2

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