Find the Domain 6x-4y=13+xy

Problem

6*x−4*y=13+x*y

Solution

1. Isolate the terms containing y on one side of the equation to express y as a function of x

6*x−13=x*y+4*y

2. Factor out the common variable y from the right side of the equation.

6*x−13=y*(x+4)

3. Solve for y by dividing both sides by the expression (x+4)

y=(6*x−13)/(x+4)

4. Identify the restriction for a rational function, which is that the denominator cannot be equal to zero.

x+4≠0

5. Determine the excluded value by solving the inequality for x

x≠−4

6. Express the domain in interval notation, representing all real numbers except −4

(−∞,−4)∪(−4,∞)

Final Answer

Domain:(−∞,−4)∪(−4,∞)

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