Given the functions

Question

Given the functions f(x)=x²-4 and g(x)=x²-3x+2 determine a simplified equation for h(x)=f(x)/g(x) 

Answer 1

h=(x+2)/(x-1);   undefined when x = 1

Answer 2

Notice that you can factor the expressions for both f(x) and g(x)

 

f(x) = x² - 4 = (x + 2) (x - 2)

g(x) = x² - 3x + 2 = (x - 1) (x - 2)

 

So h(x) = f(x) / g(x) =

(x²-4) / (x²-3x+2) =

[(x + 2) (x - 2)] / [(x - 1) (x - 2)]

 

Now you can cancel out the x-2 term, and you are left with:

 

h(x) = (x + 2) / (x - 1)

 

HOWEVER...  This is not exactly true.  When x = 2, the numerator of h(x) and the denominator are both equal to 0.  That means that h(x) is not defined for x = 2.  However, the simplified expression IS defined for x = 2.  So you have to make sure that you explicitly exclude x = 2 from the domain of h(x) when you use the simplified expression.