Find the Domain x^2y+xy=1

Problem

x2*y+x*y=1

Solution

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

2. Factor out y from the left side of the equation.

y*(x2+x)=1

3. Divide both sides by x2+x to solve for y

y=1/(x2+x)

4. Identify the values of x that make the denominator equal to zero, as these are excluded from the domain.

x2+x=0

5. Factor the quadratic expression to find the roots.

x*(x+1)=0

6. Solve for x to find the vertical asymptotes or points of discontinuity.

x=0

x=−1

7. State the domain as all real numbers except for the values found in the previous step.

Final Answer

Domain:{[x∈ℝ,x≠0,x≠−1]}

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