Divide. square root of -18 / square root of -50
1 answer:
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First, , and if we multiply
by
we get
Subtracting this from the numerator gives a remainder of
Next, , and if we multiply
by
we have
and subtracting this from the previous remainder, we end up with a new remainder of
Next, , and if we multiply
by
we get
Subtracting from the previous remainder, we get a new remainder of
which contains no more factors of , so we're done.
So,
Recall that a rational function:
has a vertical asymptote at x₀ if and only if:
Also, the roots of the above rational function are the same as P(x).
Since the rational function has a vertical asymptote at x=-1, we get that its denominator must be:
Since the rational function has a double zero at x=2 we get that its numerator must be of the form:
Finally, since the rational function has y-intercept at (0,2) we get that:
Simplifying the above equation we get:
Dividing the above equation by 4 we get:
Therefore, the rational function that satisfies the given conditions is:
Answer:
The numerator is:
The denominator is: