Rational expression: addition and subtraction

[silverdragon316]

I have this problem: I think I have it right. I hope. I have been racking my brains to understand this but it hard. I just don't have the mind set for math.

The problem is:

2 -3x-1 +5
x^5--x^2-25--x+5
then

2times x+5 - 3x-1 + 5 times x-5
(x-5) times x+5 - (x+5)(x-5) + x+5 times x-5

then

2x+ 10 - 3x-1 + 5x-25
(x-5)(x+5) (x-5)(x+5) (x-5)(x+5)

then

2x+ 10 - 3x-1 +5x-25
(x-5)(x+5)


Then

4x-16
(x-5)(x+5)

I hope this is the answer.

 

[stapel]

The problem is:...

What were the instructions for the exercise? (Expressions, in and of themselves, are not "questions". The instructions, as mentioned in other threads, are necessary to have a "question" to answer.)

2 - 3x-1 + 5
x-5 - x^2-25 + x+5

As mentioned elsewhere, multi-line formatting almost never works, and trying to use spaces to "force" the formatting isn't working in this thread any more than it's worked in any of your others. Please use standard web-safe formatting, as explained in "Karl's Notes" (in the "Forum Help" pull-down menu at the very top of every forum page), or else learn LaTeX.

Do you perhaps mean the following?

. . . . .\(\displaystyle \L \frac{2}{x\, -\, 5}\, -\, \frac{3x\, -\, 1}{x^2\, -\, 25}\, +\, \frac{5}{x\, +\, 5}\)

Please reply with correction or confirmation, followed by a clear (that is, legible) listing of your steps and reasoning thus far.

Thank you.

Eliz.

 

[silverdragon316]

I have this problem: I think I have it right. I hope. I have been racking my brains to understand this but it hard. I just don't have the mind set for math.

The problem is:

2 - 3x-1 + 5
x-5 - x^2-25 + x+5

then

2times x+5 - 3x-1 + 5 times x-5
(x-5) times x+5 - (x+5)(x-5) + x+5 times x-5

then

2x+ 10 - 3x-1 + 5x-25
(x-5)(x+5) (x-5)(x+5) (x-5)(x+5)

then

2x+ 10 - 3x-1 +5x-25
(x-5)(x+5)


Then

4x-16
(x-5)(x+5)

I hope this is the answer.

yes, that is what I mean. I am sorry that I am not clear. I didn't know how to make it look the right way. I will try to start doing it properly. My apologies and thank you.

 

[soroban]

Hello, silverdragon316!

You seem to understand the procedure . . . good work!

You made an error in the subtraction, though.

\(\displaystyle \L\frac{2}{x\,-\,5}\,-\.\frac{3x\,-\,1}{x^2\,-\,25}\,+\,\frac{5}{x\,+\,5}\)

Then: \(\displaystyle \L\:\frac{2}{x\,-\,5}\cdot\frac{x\,+\,5}{x\,+\,5}\:-\:\frac{3x\,-\,1}{(x\,-\,5)(x\,+\,5)} \:+\:\frac{5}{x\,+\,5}\cdot\frac{x\,-\,5}{x\,-\,5}\)

Then: \(\displaystyle \L\:\frac{2x\,+\,10}{(x\,-\,5)(x\,+\,5)}\:-\:\frac{3x\,-\,1}{(x\,-\,5)(x\,+\,5)} \:+\:\frac{5x\,-\,25}{(x\,-\,5)(x\,+\,5)}\)

. . . . . . . . . . . . . . . . ↓ no
Then: \(\displaystyle \L\:\frac{2x\,+\,10\,-\,3x\,-\,1\,+\,5x\,-\,25}{(x\,-\,5)(x\,+\,5}\)

Be careful . . .

You had: \(\displaystyle \L\:\frac{(2x\,+\,10)\,-\,(3x\,-\,1)\,+\,(5x\,-\,25)}{(x\,-\,5)(x\,+\,5)}\)

. . . . . . - . . . - . . . . .↓
Then: \(\displaystyle \L\:\frac{2x\,+\,10\,-\,3x\,+\,1\,+\,5x\,-\,25}{(x\,-\,5)(x\,+\,5)} \;=\;\frac{4x\,-\,14}{(x\,-\,5)(x\,+\,5)}\)