The solutions when y = 0 are x = -4.796 and x = 4.796
The graph of the function
The function is given as:
[tex]y = (\frac{x + 5}{x + 1} \div \frac{(x + 3)(x - 2)}{(x -4)(x + 1)})- \frac{1}{x - 2}[/tex]
See attachment for the graph of the function
The vertical asymptote
When the function is simplified, we have:
(x +3)(x -2) at the denominator of one of the terms
Set this factor to 0
(x +3)(x -2) = 0
Expand
x + 3 = 0 and x -2 = 0
Solve for x
x = -3 and x = 2
Hence, the vertical asymptotes are x = -3 and x = 2
The feature at x = -1
The feature at x = -1 is a hole and, not a vertical asymptote.
This is so because the absolute value of -1 is less than the absolute values of the vertical asymptotes at x = -3 and x = 2
The solution when y = 0
From the attached graph, we have:
x = -4.796 and x = 4.796 when y = 0
Hence, the solutions when y = 0 are x = -4.796 and x = 4.796
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