Adding Rational Expressions

[XxBubbleGummxX]

I need to simplify and state all non permissible values for this equation:

x-2/x+1 + x-1/x^2-1

 

[stapel]

I need to simplify and state all non permissible values for this equation:

x-2/x+1 + x-1/x^2-1

What you have posted means the following:

. . . . .\(\displaystyle x\, -\, \frac{2}{x}\, +\, 1\, +\, x\, -\, \frac{1}{x^2}\,-\, 1\)

However, I suspect that you really mean this:

. . . . .\(\displaystyle \frac{x\, -\, 2}{x\, +\, 1}\, +\, \frac{x\, -\, 1}{x^2\, -\, 1}\)

Either way, you can refresh on the topic here. Once you've learned the basic terms and techniques, please attempt the exercise. If you get stuck, you can then reply with (1) confirmation or correction of what the actual expression is and (2) a clear listing of your efforts so far.

Thank you!

 

[Quaid]

Kindly follow the boards' posting guidelines, including the statement at the bottom of that summary page regarding Order of Operations.

Let us know, if you don't understand what stapel posted above about your typing.

Thank you! :cool:

 

[XxBubbleGummxX]

The Second one is the correct equation and I can figure out how to factor besides the face that (x^2-1) is a difference of squares

 

[Quaid]

The Second one is the correct equation

Thank you for confirming this. Use proper grouping symbols, in future posts, and this will no longer be an issue.

I [can't] figure out how to factor besides the [fact] that (x^2-1) is a difference of squares

That difference of squares is the only polynomial that factors, in this exercise.

Next, do you see the cancellation of factors waiting to happen?

 

[XxBubbleGummxX]

Does that mean that what I'm left with after I've factored the difference of squares, and canceled out the things that are alike, Im left with (x-2) as my answer?

 

[JeffM]

Does that mean that what I'm left with after I've factored the difference of squares, and canceled out the things that are alike, Im left with (x-2) as my answer?

No. The factoring and cancelling are just to make things easier to work with.

Let's go back to the original question

I need to simplify and state all non permissible values for this equation:

(x-2)/(x+1) + (x-1)/(x^2-1) I inserted the needed parentheses.

Now this is a bit of a trick question because to answer the second part fully you DON'T simplify first.

A fraction cannot have a denominator of 0. So at what value or values of x is (x + 1) = 0? And at what value or values of x is (x² - 1) = 0?

Sneaky bunch, those teachers.

Now back to the addition, where you do simplify where possible.

\(\displaystyle \dfrac{x - 2}{x + 1} + \dfrac{x - 1}{x^2 - 1} = \dfrac{x - 2}{x + 1} + \dfrac{(x - 1) * 1}{(x - 1)(x + 1)} = \dfrac{x - 2}{x + 1} + \dfrac{1}{x + 1} = what?\)

How do you add fractions that have a common denominator? See. These are not that hard; they are just new and scary looking. Go step by step and be careful.