SOLUTION: For each rational function, identify any holes or horizontal or vertical asymptotes of its graph. 1) y= (x+3)/(x+2)(x+3) 2) y= x+5/(x-2)(x-3)

Question 740836: For each rational function, identify any holes or horizontal or vertical asymptotes of its graph.
1) y= (x+3)/(x+2)(x+3)
2) y= x+5/(x-2)(x-3)
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
1)

asymptotes will occur for which make the denominator . For this equation the denominator will be zero if . So the vertical lines, will be for this equation.
For this equation, when become very large, the fraction approaches in value.
so, is asymptote

2.
or

"Holes" would occur when the numerator and denominator have a common factor which is an expression which could be zero.
Since this fraction has such , there will be no "holes".
asymptotes will occur for which make the denominator . For this equation the denominator will be zero if or . So the vertical lines, and will be for this equation.
asymptotes will occur if approaches some constant value when become (positive or negative).
For this equation, when become very large, the denominator of the fraction becomes very large.
This makes the fraction very, very . In fact the fraction approaches in value.
So as become very large, the fraction becomes negligible and the approaches .

RELATED QUESTIONS
Hi heres one more.. For each rational function, identify any holes or horizontal or... (answered by checkley77)

Hi could you help me with this? For each rational function, identify any holes or... (answered by checkley77)

For each rational function, identify any holes or horizontal or vertical asymptotes of... (answered by stanbon)

For each rational function, identify any holes or horizontal or vertical asymptotes of... (answered by jim_thompson5910)

find the rational fraction, identify any holes or horizontal or vertical asymptotes of... (answered by richard1234)

hey i need help with this problem...... For each rational function, identify any holes (answered by checkley77,JSmall)

For each rational function, identify any holes or horizontal or vertical asymptotes of... (answered by stanbon)

determine any horizontal or vertical asymptotes or holes for... (answered by richwmiller)

For each rational function, identify any holes or horizontal or vertical asymptotes of... (answered by RAY100)