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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

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)

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.

dwc

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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

Chris,

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.

dwc