SOLUTION: perform indicated operation, simplifying if possible. x^2+3x-4/x^2-x-20 * 5x-25/5x^2-x please show step by step. also what is the difference between X^2+3x-4 and X^2-3x-4 how do y

Question 201758: perform indicated operation, simplifying if possible.
x^2+3x-4/x^2-x-20 * 5x-25/5x^2-x please show step by step. also what is the difference between X^2+3x-4 and X^2-3x-4 how do you factor them I came up with (x+1)(x-4)
Answer by PRMath(133) (Show Source): You can put this solution on YOUR website!
perform indicated operation, simplifying if possible.
x^2+3x-4/x^2-x-20 * 5x-25/5x^2-x please show step by step. also what is the difference between X^2+3x-4 and X^2-3x-4 how do you factor them I came up with (x+1)(x-4)

Ok, first think back to grade school math for a second, because these concepts connect, k? Remember that 4/4 equals 1, right? That's one concept to keep in your mind.

Another concept is that you can cancel out FACTORS (multiplication) in a fraction. For example: 4x/4 means that you can look at 4/4 and realize it equals 1 and then that just leaves the "x".

Now that you have those thoughts in your head, let's look at your problem.

It is this:
x^2+3x-4/x^2-x-20 * 5x-25/5x^2-x

So I would first factor everything I could factor. Let's start with:
x^2+3x-4. You have to think, what can you use that will MULTIPLY to get "-4" yet at the same time, will ADD up to equal "+3".
So, let's factor in this way: (x + 4)(x - 1)
Remember FOIL? Check to see if we factored correctly.

Let's now factor: x^2-x-20
Sooooo what can you do that will MULTIPLY to get "-20" yet at the same time, will ADD up to be "-1"?
We can factor the equation this way: (x - 5)(x + 4)

We are not done yet. Now we have to factor: 5x-25
Do you see a number there that is common to both the "5" and the "25"???
How about the number "5"?
SOooo let's factor this way: 5(x - 5)

We are STILL not done. Now we have to factor: 5x^2-x

What is common to the 5x^2 and the "X"????? How about "x"??
So, let's factor this way: x(5x - 1)

Wow, we just did a lot of factoring. Now will will put that info all together to see what we can cancel out, k?
Here we go:

(x + 4)(x - 1) 5(x - 5)
________________________________
(x - 5)(x + 4) x(5x - 1)

The above is the SAME problem you wrote, but everything has been factored out. Now we can do some canceling. I'm not sure how to show this to you. I really want to highlight the cancellations or do a strike over. Hmmmm.

(x + 4)(x - 1) 5(x - 5)
_________________________
(x - 5)(x + 4) x(5x - 1)

I think the only thing I can do is tell you in this way:
(x+4)in the numerator cancels out (x+4) in the denominator.
(x-5) in the numerator cancels out (x-5) in the denominator.
Now you are left with:
(x - 1)5
_________
x(5x - 1)
You cannot cancel out the "X" variables, because in the numerator (x - 1) is not factorable.
So your answer is(assuming I understood what you wrote as the question) is:

5(x - 1)
_________
x(5x - 1)

You also wanted to know: what is the difference between
X^2+3x-4 and X^2-3x-4. How do you factor them? I came up with (x+1)(x-4)

Here's your first equation: X^2+3x-4
Think of this: What can you MULTIPLY to get "-4" and yet ADD to get "+3"
It would factor like this: (x +4)(x-1)

Here's your 2nd equation: X^2-3x-4
Again, what can you MULTIPLY to get "-4" and yet ADD to get a "-3". (In the previous problem, you wanted a POSITIVE 3 but this time you want a NEGATIVE 3).
This 2nd equation would factor like this: (x -4)(x +1)
Good luck. Hope this helps. :-)
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