Can someone help me on this question. I don’t get how I’m supposed to proceed because one of the equations equals 0/0

Question

Define a function f-> R -> R as follows, where c is a constant:

f(x)= ((square root of (x^2 + 5x) -6)/ (x^2-9x+20) if x<4

And

(x^2-cx-9)/(2x+4) if x >= 4

What value of c is needed to make f a continuos function

Answer 1

Use l'Hospital's rule on the expression to the left of 4...to get a removable discontinuity with value = -13/12.

Then set f(4)=-13/12 to find c so that f will be continuous.