Solving Rational Expressions and Complex Fractions - Help and Tips

[elie_girl]

I keep getting the answers to these problems wrong.

1)For what numbers is the rational expression undefined? (If there are less than two answers, enter NONE in any extra boxes.) x/x^2-2x-24
x=_____ Smaller value
x=_____ Larger Value

2)Simplify the complex fraction. 3m-6/5m/4m-8/25
I got the answer 3/500m and I still got it wrong

3)Perform the operation. Write the answer without negative exponents. Assume that all variables represent positive real numbers. (If the simplification is an imaginary number, enter IMAGINARY.) (-27/8n^6)^-2/3

 

[Ichiro101]

The trick to do number one is that, you CANNOT divide any number by 0, so that means, let's say you have a rational function, y/t, t cannot be any value equal to 0. So, in this case, x/x^2-2x-24, you have to equate (x^2-2x-24) to 0, and when you factor that you should get (x+4)(x-6)=0. So remember, when you come across any questions like this, equate the function that is being divided to 0, and you should get your answer.

For number 2, if you do not know what m is, then you cannot express your answer as 3/500m, think about it.
When you divide a/b by c/d, it's same as saying a/b multiplied by d/c. If you follow that logic, then your fraction can be written as:
(3m-6)/5m mutiplied by 25/(4m-8), which you get (15m-30)/(4m-8)

I have no idea how you got 3/500m, because there is no way to cancel all the terms here if I'm understanding your question right.

3. All you have to do is take the inverse of your fraction, and you'll get rid of your negative exponents, because (a/b)^-n is the same as (b/a)^n

 

[elie_girl]

Oh ok. I think I understand it now a little better. Thanks. I'll try and follow those steps and see what I get. Thanks again.