Write as a Function of x x^2-xy=4

$x^{2} - x y = 4$

Step 1

Subtract $x^{2}$ from both sides of the equation.

$- x y = 4 - x^{2}$

Step 2

Divide each term in $- x y = 4 - x^{2}$ by $- 1 x$ and simplify.

Divide each term in $- x y = 4 - x^{2}$ by $- 1 x$ .

$\frac{- x y}{- 1 x} = \frac{4}{- 1 x} + \frac{- x^{2}}{- 1 x}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x y}{x} = \frac{4}{- 1 x} + \frac{- x^{2}}{- 1 x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x y}{x} = \frac{4}{- 1 x} + \frac{- x^{2}}{- 1 x}$

Divide $y$ by $1$ .

$y = \frac{4}{- 1 x} + \frac{- x^{2}}{- 1 x}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{4}{x} + \frac{- x^{2}}{- 1 x}$

Dividing two negative values results in a positive value.

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

Cancel the common factor of $x^{2}$ and $x$ .

Factor $x$ out of $x^{2}$ .

$y = - \frac{4}{x} + \frac{x \cdot x}{x}$

Cancel the common factors.

Raise $x$ to the power of $1$ .

$y = - \frac{4}{x} + \frac{x \cdot x}{x^{1}}$

Factor $x$ out of $x^{1}$ .

$y = - \frac{4}{x} + \frac{x \cdot x}{x \cdot 1}$

Cancel the common factor.

$y = - \frac{4}{x} + \frac{x \cdot x}{x \cdot 1}$

Rewrite the expression.

$y = - \frac{4}{x} + \frac{x}{1}$

Divide $x$ by $1$ .

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

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.

$f (x) = - \frac{4}{x} + x$

Write as a Function of x x^2-xy=4

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