Rational Expression

Question

Please answer the following 3 questions:

1) Find the value(s) of x for which the rational expression      x        is undefined, and explain why it would be undefined.

                                                                                     x² -25  

2) When simplifying the rational expression         x-7             , is the answer 1 or -1. Explain your decision.
                                                                       7-x

 

3) What is a vertical asymptote of a rational function?

Answer 1

1.  if the rational expression is just x  divided by (x²-25), and x is any Real number, then it's undefined if x = ±5 because zeros cannot be allowed in the entire denominator

2. since the numerator and denominator are opposites, this expression can be simplified to -1, COUPLED WITH THE PROVISO THAT x ≠ 7; this exclusion must remain even though the simplification occurred.

3. A vertical asymptote of a rational algebraic function occurs whenever a zero would occur in the original denominator, except for the case of a HOLE.  A hole corresponds to a cancelled factor that was identical in both original denominator and numerator.  That is, V.A. is associated with a zero of a remaining denominator factor, after simplifications. A V.A., of course, represents a discontinuity in the graph, showing that the graph tends toward ±infinity as x approaches a value that is not in the domain.