Find the Domain x^2-x+1÷(x^2)+x+1=(14(x-1))÷13(x+1)

Problem

x2−x+1/(x2)+x+1=(14*(x−1))/(13*(x+1))

Solution

1. Identify the denominators in the equation to determine where the expression is undefined.

2. Set the first denominator x2 to zero to find the values that must be excluded from the domain.

x2=0

3. Solve for x in the first denominator.

x=0

4. Set the second denominator 13(x + 1)$ to zero to find additional excluded values.

13*(x+1)=0

5. Solve for x in the second denominator.

x+1=0

x=−1

6. Combine the restrictions to state the domain, which includes all real numbers except those that make any denominator zero.

Final Answer

Domain: *{[x∈ℝ,x≠0,x≠−1]}

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