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I try to use the following theorem: If f is continuous on [a,b] and if f(a) and f(b) are nonzero and have opposite signs, then there is at least one solution of the equation f(x) = 0 in the interval (a,b).

As the theorem requires f to be continuous on the closed interval [2,4], the open interval (2,4) is what is given, indeed there is a discontinuity at x=2 and at x =4. The equation can be rewritten as [tex] \frac{x-2}{x-4} + \frac{c}{d}=0 [/tex] x not equal to 2. I do not know of any other theorem to use. Can someone point me in the correct direction, please. Thank you.