Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

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

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

Step 1.2

Subtract $6$ from both sides of the equation.

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

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Rewrite the expression.

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

Step 3.2.2

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

Tap for more steps...

Step 3.2.2.1

Cancel the common factor.

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

Step 3.2.2.2

Divide $x$ by $1$ .

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

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Simplify each term.

Tap for more steps...

Step 3.3.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.3.1.1.1

Cancel the common factor.

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

Step 3.3.1.1.2

Rewrite the expression.

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

Step 3.3.1.2

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

Tap for more steps...

Step 3.3.1.2.1

Factor $3$ out of $- 6$ .

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

Step 3.3.1.2.2

Cancel the common factors.

Tap for more steps...

Step 3.3.1.2.2.1

Cancel the common factor.

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

Step 3.3.1.2.2.2

Rewrite the expression.

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

Step 3.3.1.3

Move the negative in front of the fraction.

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

Step 3.3.2

Combine the numerators over the common denominator.

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

Step 4

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

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