Write as a Function of x 6xy-3x-3y+6=0

$6 x y - 3 x - 3 y + 6 = 0$

Step 1

Move all terms not containing $y$ to the right side of the equation.

Add $3 x$ to both sides of the equation.

$6 x y - 3 y + 6 = 3 x$

Subtract $6$ from both sides of the equation.

$6 x y - 3 y = 3 x - 6$

Step 2

Factor $3 y$ out of $6 x y - 3 y$ .

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

$3 y (2 x) - 3 y = 3 x - 6$

Factor $3 y$ out of $- 3 y$ .

$3 y (2 x) + 3 y (- 1) = 3 x - 6$

Factor $3 y$ out of $3 y (2 x) + 3 y (- 1)$ .

$3 y (2 x - 1) = 3 x - 6$

Step 3

Divide each term in $3 y (2 x - 1) = 3 x - 6$ by $3 (2 x - 1)$ and simplify.

Divide each term in $3 y (2 x - 1) = 3 x - 6$ by $3 (2 x - 1)$ .

$\frac{3 y (2 x - 1)}{3 (2 x - 1)} = \frac{3 x}{3 (2 x - 1)} + \frac{- 6}{3 (2 x - 1)}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y (2 x - 1)}{3 (2 x - 1)} = \frac{3 x}{3 (2 x - 1)} + \frac{- 6}{3 (2 x - 1)}$

Rewrite the expression.

$\frac{y (2 x - 1)}{2 x - 1} = \frac{3 x}{3 (2 x - 1)} + \frac{- 6}{3 (2 x - 1)}$

Cancel the common factor of $2 x - 1$ .

Cancel the common factor.

$\frac{y (2 x - 1)}{2 x - 1} = \frac{3 x}{3 (2 x - 1)} + \frac{- 6}{3 (2 x - 1)}$

Divide $y$ by $1$ .

$y = \frac{3 x}{3 (2 x - 1)} + \frac{- 6}{3 (2 x - 1)}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $3$ .

Cancel the common factor.

$y = \frac{3 x}{3 (2 x - 1)} + \frac{- 6}{3 (2 x - 1)}$

Rewrite the expression.

$y = \frac{x}{2 x - 1} + \frac{- 6}{3 (2 x - 1)}$

Cancel the common factor of $- 6$ and $3$ .

Factor $3$ out of $- 6$ .

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

Cancel the common factors.

Cancel the common factor.

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

Rewrite the expression.

$y = \frac{x}{2 x - 1} + \frac{- 2}{2 x - 1}$

Move the negative in front of the fraction.

$y = \frac{x}{2 x - 1} - \frac{2}{2 x - 1}$

Combine the numerators over the common denominator.

$y = \frac{x - 2}{2 x - 1}$

Step 4

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = \frac{x - 2}{2 x - 1}$

Write as a Function of x 6xy-3x-3y+6=0

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