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Algebra II with Trig Ch1.4 #25


We need help on Algebra II with Trig 1.4 #25. How do we get started?



We want to reduce the problem. 

The first step I take on these kind of problems is to make it easier to see. Looking at what we are given – we can see that the we have two big parts added together in the numerator

One part is the


and the other part is the


We can see that both parts have an x+4. 

Often in busy problems like this, we can make things easier and replace the x+4 with k to get something like

-2xk^3 – 3(3-x^2)k^k

as the numerator. So now we can see we can factor out the k. 

k^2 [-2xk – 3(2-x^2)]


We can put this back to get 

(x+4)^2 [-2x(x+4) – 3(2-x^2)]  /  [ (x+4)^6]

Now we can reduce by dividing out the (x+4)^2 term to get

[-2x(x+4) – 3(2-x^2)]  /  [ (x+4)^2]