Question

Need the answer in 20 mins

Answer 1

Discontinuity occurs at asymptotes

Find the vertical asymptotes

• x²-9=0
• (x+3)(x-3)=0
• x=±3

Simplify the function

• x-3/(x+3)(x-3)
• 1/x+3

x=3 is removable

Answer 2

• x = - 3 or x = 3
• x = 3 is removable

Explanation:

Given function is discontinuous when the denominator is zero:

• x² - 9 = 0
• x² = 9
• x = √9
• x = 3 or x = - 3

If you simplify the function:

• f(x) = (x - 3) / (x² - 9) = (x - 3) / (x - 3)(x + 3) = 1 / (x + 3)

Then the new function will have one of the discontinuity (x = 3) removed.