Solve for x (x^2-9)/(x^2-4x-5)=0

Problem

(x2−9)/(x2−4*x−5)=0

Solution

1. Identify the condition for a fraction to equal zero. A rational expression is zero only when its numerator is zero and its denominator is non-zero.

2. Set the numerator equal to zero and solve for x

x2−9=0

x2=9

x=±3

3. Factor the denominator to identify values that must be excluded from the domain to avoid division by zero.

x2−4*x−5=(x−5)*(x+1)

4. Determine the excluded values by setting the denominator factors to zero.

x−5≠0⇒x≠5

x+1≠0⇒x≠−1

5. Verify the solutions found in step 2 against the excluded values. Since 3 and −3 are not equal to 5 or −1 both are valid solutions.

Final Answer

(x2−9)/(x2−4*x−5)=0⇒x=3,−3

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