# For what values of x, if any, does #f(x) = 1/((5x+8)(x-6) # have vertical asymptotes?

##### 1 Answer

#### Explanation:

For a rational function such as the one presented, vertical asymptotes occur whenever the denominator of the function is equal to

Now, we must find the times when

#(5x+8)(x-6)=0#

What we have here are two terms,

Thus, to find the times when the whole expression equals

#5x+8=0#

#5x=-8#

#x=-8/5# There is a vertical asymptote at

#x=-8/5# .

#x-6=0#

#x=6# There is a vertical asymptote at

#x=6# .

We can check a graph of the original function:

graph{1/((5x+8)(x-6)) [-7.75, 12.25, -4.915, 5.085]}