SOLUTION: Im taking a course online, and I couldn't be more confused. There's no teacher, and I have no idea where to even start. If someone could show me the steps to solving these equation

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Im taking a course online, and I couldn't be more confused. There's no teacher, and I have no idea where to even start. If someone could show me the steps to solving these equation      Log On


   



Question 969518: Im taking a course online, and I couldn't be more confused. There's no teacher, and I have no idea where to even start. If someone could show me the steps to solving these equations with the two examples I provided, I would really appreciate it. Thank you sooo much!
They ask me to simplify and state the restrictions on the variable. (dividing rational expressions)
1. x^2-x-6 over x^2- 4 / x^2-2x+1 over x^2-1
2. 2x over 9x^2 +15x - 8 over 3x + 5

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
#2:

The best I can make of your description:

%28%282x%29%2F%289x%5E2%2B15x-8%29%29%2F%283x%2B5%29

highlight_green%28%282x%29%2A%283x%2B5%29%2F%289x%5E2%2B15x-8%29%29
but WHAT do you want with it? This is not an equation, so nothing to "solve".

Denominator: (3x 8)(3x 1)----none of these...
(9x 8)(x 1)------none of these....
The denominator is apparently not factorable. (More combinations were checked than those shown).(Try checking the discriminant, since the graph below means that there ARE two vertical asymptotes. This means, use general solution of quadratic formula to find zeros of the denominator.)

Your rational expression has two x-intercepts: 0 and 1%2F3. The degree of numerator and denominator both are two; so expect the leading terms of numerator and denominator to give unbound behavior of x to positive or negative infinity as %286x%5E2%29%2F%289x%5E2%29=6%2F9=2%2F3 or a horizontal asymptote of y=2%2F3.

A few other details about the rational expression can also be examined.

Expect a graph like this:
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C%282x%29%2A%283x%2B5%29%2F%289x%5E2%2B15x-8%29%29