Given #f(x)=x+2, g(x)=x-3, h(x)=x+4# how do you determine #y=(f(x))/(h(x))times(g(x))/(h(x))#?

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Answer 1 · 2017-07-01T11:16:13

#y = frac(x^(2) - x - 6)(x^(2) + 8 x + 16)#

We have: #y = frac(f(x))(h(x)) times frac(g(x))(h(x))#

#Rightarrow y = frac(f(x) times g(x))((h(x))^(2))#

Let's substitute the expressions for #f(x)#, #g(x)# and #h(x)# into the equation:

#Rightarrow y = frac((x + 2) times (x - 3))((x + 4)^(2))#

Then, let's expand the parentheses:

#Rightarrow y = frac(x^(2) + 2 x - 3 x - 6)(x^(2) + 4 x + 4 x + 16)#

#therefore y = frac(x^(2) - x - 6)(x^(2) + 8 x + 16)#