Find the Domain 2/(x+2)+1/(x+4)=4/(x^2+6x+8)

Problem

2/(x+2)+1/(x+4)=4/(x2+6*x+8)

Solution

1. Identify the denominators in the equation. The domain of a rational expression consists of all real numbers except those that make any denominator equal to zero.

2. Factor the quadratic denominator on the right side of the equation.

x2+6*x+8=(x+2)*(x+4)

3. Set each unique factor in the denominators to zero to find the excluded values.

x+2=0

x+4=0

4. Solve for x to identify the values that must be excluded from the domain.

x=−2

x=−4

5. State the domain as all real numbers except for the excluded values. In interval notation, this excludes the points where the function is undefined.

Final Answer

Domain: *(−∞,−4)∪(−4,−2)∪(−2,∞)

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