Write as a Function of x xy+3y=2x+1

$x y + 3 y = 2 x + 1$

Step 1

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

Factor $y$ out of $x y$ .

$y x + 3 y = 2 x + 1$

Factor $y$ out of $3 y$ .

$y x + y \cdot 3 = 2 x + 1$

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

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

Step 2

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

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

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

Simplify the left side.

Cancel the common factor of $x + 3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

$y = \frac{2 x}{x + 3} + \frac{1}{x + 3}$

Simplify the right side.

Combine the numerators over the common denominator.

$y = \frac{2 x + 1}{x + 3}$

Step 3

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.

$f (x) = \frac{2 x + 1}{x + 3}$

Write as a Function of x xy+3y=2x+1

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