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Algebra 1 Ch11.5 #11

Question from Josh:

I’m doing Jacob’s Elementary Algebra and I’m having difficulty on Lesson 11-5 problem 11. I don’t understand how to simplify the problem by looking for common factors. Would you be able to provide any help?
Thank You

Answer from Dr. Callahan:

You have to take these in steps.

For a) you first look for something to simplify. You could multiply things out – but that would not help. Yet, if you look at the

x^2 – y^2 term you might remember (page 470) difference of two squares – which will help you remember that this is

(x-y) (x+y)

which now will help you factor the rest

In b) you could take the 4x^2 + 2x and make it 2x(2x+1) which will help

in c) you can make the x^2-25 = (x+5)(x-5) like in a. You can also factor the x^2 – 10x +25 to get (x – 5)(x – 5)

in d) you can factor out the first numerator to get x (x^2+3) and then factor it out.

You just need to play with each term first and then see what cancels out. You might can do more that I have done here – but this should get you started.


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Algebra 1 Ch11.2 #5

Question from Chris:

Algebra 1 chapter 11 lesson 2 problem 5h:
I see that you can cross out the (x + 7) in the numerator & denominator to get 3 /(x +3). Why can’t you simplify further by cancelling 3/3 so that the final answer is 1/x? Thanks

Answer from Dr. Callahan:


You must handle everything added together as one.

Because when you divide 3 by x+ 3 = you cannot simplify

For instance, simplifying is all about making a simpler form, but the answer is still the same.

If you have 3/3x and you let x=1, the answer is just 3

If you simply 3/3x tp 1/x and let x = 1, you still get one.

Simplifying does not change the problem.

Now in your case, try to set x=1.

3/(x+3) when x =1 is 3/4

but if we change to 1/x and let x=1, you get 1. So you know it is wrong.

Hope this helps.