Answer:
x = 3 or x = 12
Explanation:
You want the possible values of x that make it true that ...
(x +1)²/(x -2) = 16 +(x -3)/(x -2)
Division expression
The given division expression can be written in terms of quotient and remainder as ...
p/q = a +r/q ⇒ p = aq +r
Application
Here, this means ...
(x +1)² = 16(x -2) +(x -3)
x² +2x +1 = 16x -32 +x -3
x² -15x = -36
x² -15x +56.25 = 20.25 . . . . . complete the square
(x -7.5)² = 4.5²
x = 7.5 ± 4.5 . . . . . . . . . . . . . take the square root, add 7.5
x = 3 or 12
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Additional comment
The given quotient-remainder equation has a vertical asymptote at x = 2. When we write it as f(x) = 0, the graph of f(x) is symmetrical about the point (2, -11).