Solve the Rational Equation for x (3x-4)/(x-5)=(3x+6)/(x+2)

$\frac{3 x - 4}{x - 5} = \frac{3 x + 6}{x + 2}$

Factor each term.

Factor $3$ out of $3 x + 6$ .

Factor $3$ out of $3 x$ .

$\frac{3 x - 4}{x - 5} = \frac{3 (x) + 6}{x + 2}$

Factor $3$ out of $6$ .

$\frac{3 x - 4}{x - 5} = \frac{3 x + 3 \cdot 2}{x + 2}$

Factor $3$ out of $3 x + 3 \cdot 2$ .

$\frac{3 x - 4}{x - 5} = \frac{3 (x + 2)}{x + 2}$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{3 (x + 2)}{x + 2}$ by cancelling the common factors.

Cancel the common factor.

$\frac{3 x - 4}{x - 5} = \frac{3 (x + 2)}{x + 2}$

Rewrite the expression.

$\frac{3 x - 4}{x - 5} = \frac{3}{1}$

Divide $3$ by $1$ .

$\frac{3 x - 4}{x - 5} = 3$

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.

$x - 5, 1$

Remove parentheses.

$x - 5, 1$

The LCM of one and any expression is the expression.

$x - 5$

Multiply each term in $\frac{3 x - 4}{x - 5} = 3$ by $x - 5$ to eliminate the fractions.

Multiply each term in $\frac{3 x - 4}{x - 5} = 3$ by $x - 5$ .

$\frac{3 x - 4}{x - 5} (x - 5) = 3 (x - 5)$

Simplify the left side.

Cancel the common factor of $x - 5$ .

Cancel the common factor.

$\frac{3 x - 4}{x - 5} (x - 5) = 3 (x - 5)$

Rewrite the expression.

$3 x - 4 = 3 (x - 5)$

Simplify the right side.

Apply the distributive property.

$3 x - 4 = 3 x + 3 \cdot - 5$

Multiply $3$ by $- 5$ .

$3 x - 4 = 3 x - 15$

Solve the equation.

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

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

$3 x - 4 - 3 x = - 15$

Combine the opposite terms in $3 x - 4 - 3 x$ .

Subtract $3 x$ from $3 x$ .

$0 - 4 = - 15$

Subtract $4$ from $0$ .

$- 4 = - 15$

Since $- 4 \neq - 15$ , there are no solutions.

No solution

Solve the Rational Equation for x (3x-4)/(x-5)=(3x+6)/(x+2)

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