Find the Domain y-3=y(x+4)

Problem

y−3=y*(x+4)

Solution

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

2. Distribute the y on the right side of the equation.

y−3=y*x+4*y

3. Rearrange the terms to group all terms containing y on one side.

y−y*x−4*y=3

4. Combine like terms.

−3*y−y*x=3

5. Factor out y from the left side.

y*(−3−x)=3

6. Solve for y by dividing both sides by (−3−x)

y=3/(−3−x)

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

−3−x=0

8. Solve for x to find the excluded value.

x=−3

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

Final Answer

Domain:{[x∈ℝ,x≠−3]}

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