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# Rational Functions

A rational function can have a variable like "x" in the numerator AND the denominator. When this happens, there are some special rules and properties to consider.

# Rational Functions Problem Solving

How many real values of $$x$$ satisfy the above equation?

$$f$$ and $$g$$ are functions defined as $$f(x) = 16 + \frac{9}{x}$$ and $$g(x) = \frac{9}{x}$$. What is the value of $$(f+g)(18)$$?

What is the nearest integer value of $y=\frac{6x-23}{x-5}$ when $$x=10000$$?

$$f$$ and $$g$$ are functions defined as $$f(x)= 5x + \frac{6}{2x-2}$$ and $$g(x) = \frac{4x}{3x-2}$$. What is the value of $$\left(f\circ g\right)(4)$$?

Note: $$f \circ g$$ denotes the composition of the 2 functions.

If the asymptotes of the graph $y=\frac{7x+2}{x-2a}$ are $$x=24$$ and $$y=b$$, what is the value of $$ab$$?

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