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Given f(x)= 4x^2+6x and g(x)=2x^2+13x+15, find (f/g) (x) show your work

 Mar 10, 2019

\(f(x) = 4x^2 + 6x = 2x(2x+3)\\ \text{If this problem makes any sense at least one of these terms will be a factor of }g(x)\\ g(x) = 2x^2 + 13x + 15 = (2x+3)(x+5)\\ (f/g)(x) = \dfrac{f(x)}{g(x)} = \dfrac{2x(2x+3)}{(x+5)(2x+3)} = \dfrac{2x}{x+5}\\ \text{HOWEVER}\\ \text{There is a values of }x \text{ for which this is invalid}\\ \text{I leave it to you to identify these}\)

 Mar 10, 2019

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