Solve for x y=(2x-4)/(x-5)

$y = \frac{2 x - 4}{x - 5}$

Step 1

Rewrite the equation as $\frac{2 x - 4}{x - 5} = y$ .

$\frac{2 x - 4}{x - 5} = y$

Step 2

Factor $2$ out of $2 x - 4$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $- 4$ .

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

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

$\frac{2 (x - 2)}{x - 5} = y$

Step 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.

$x - 5$

Step 4

Multiply each term in $\frac{2 (x - 2)}{x - 5} = y$ by $x - 5$ to eliminate the fractions.

Multiply each term in $\frac{2 (x - 2)}{x - 5} = y$ by $x - 5$ .

$\frac{2 (x - 2)}{x - 5} (x - 5) = y (x - 5)$

Simplify the left side.

Cancel the common factor of $x - 5$ .

Cancel the common factor.

$\frac{2 (x - 2)}{x - 5} (x - 5) = y (x - 5)$

Rewrite the expression.

$2 (x - 2) = y (x - 5)$

Apply the distributive property.

$2 x + 2 \cdot - 2 = y (x - 5)$

Multiply $2$ by $- 2$ .

$2 x - 4 = y (x - 5)$

Simplify the right side.

Apply the distributive property.

$2 x - 4 = y x + y \cdot - 5$

Move $- 5$ to the left of $y$ .

$2 x - 4 = y x - 5 y$

Step 5

Solve the equation.

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

$2 x - 4 - y x = - 5 y$

Add $4$ to both sides of the equation.

$2 x - y x = - 5 y + 4$

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

Factor $x$ out of $2 x$ .

$x \cdot 2 - y x = - 5 y + 4$

Factor $x$ out of $- y x$ .

$x \cdot 2 + x (- y) = - 5 y + 4$

Factor $x$ out of $x \cdot 2 + x (- y)$ .

$x (2 - y) = - 5 y + 4$

Divide each term in $x (2 - y) = - 5 y + 4$ by $2 - y$ and simplify.

Divide each term in $x (2 - y) = - 5 y + 4$ by $2 - y$ .

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

Simplify the left side.

Cancel the common factor of $2 - y$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Combine the numerators over the common denominator.

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

Factor $- 1$ out of $- 5 y$ .

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

Rewrite $4$ as $- 1 (- 4)$ .

$x = \frac{- (5 y) - 1 (- 4)}{2 - y}$

Factor $- 1$ out of $- (5 y) - 1 (- 4)$ .

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

Simplify the expression.

Rewrite $- (5 y - 4)$ as $- 1 (5 y - 4)$ .

$x = \frac{- 1 (5 y - 4)}{2 - y}$

Move the negative in front of the fraction.

$x = - \frac{5 y - 4}{2 - y}$

Solve for x y=(2x-4)/(x-5)

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