Find the Domain xy+y=x^2

Problem

x*y+y=x2

Solution

1. Isolate the variable y to express it as a function of x

2. Factor the left side of the equation by taking out the common factor y

y*(x+1)=x2

3. Divide both sides by (x+1) to solve for y

y=(x2)/(x+1)

4. Identify the restriction for the domain by setting the denominator equal to zero, since division by zero is undefined.

x+1=0

5. Solve for x to find the value that must be excluded from the domain.

x=−1

6. State the domain as all real numbers except for the value that makes the denominator zero.

Final Answer

Domain:{x|x∈ℝ,x≠−1}

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