SOLUTION: I just posted this equation, but I don't think it was very clear soo hopefully this format clears up any confusion. I'm taking a course online, and I couldn't be more confused. The

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I just posted this equation, but I don't think it was very clear soo hopefully this format clears up any confusion. I'm taking a course online, and I couldn't be more confused. The      Log On


   

Question 969531: I just posted this equation, but I don't think it was very clear soo hopefully this format clears up any confusion. I'm 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 2 examples I provided, I would really appreciate it. Thanks in advance!
They ask me to simplify and state the restrictions on the variable. (Dividing/Subtracting Rational Expressions)
1. The numerator consists of x^2 - x-6, and the denominator is x^2 -4. Then we have to DIVIDE that by the numerator which is x^2 -2x+1, divided by the denominator which is x^2-1.

2. The numerator consists of 2x, and is divided by 9x^2+15x. Then we have to SUBTRACT the numerator which is 8, by the denominator which is 3x+5.

I really hope this is clear. Im not sure how else to break it down since I have no idea how to type up equations. Thanks again!




Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
#2 again according to the newer description:

%282x%29%2F%289x%5E2%2B15%29-8%2F%283x%2B5%29

The goal suggested would seem to perform addition (or subtraction) of rational expressions.

9x%5E2%2B15=3%28x%5E2%2B5%29, so you have %282x%29%2F%28%283%29%283x%2B5%29%29-8%2F%283x%2B5%29;

%282x%29%2F%28%283%29%283x%2B5%29%29-%288%2F%283x%2B5%29%29%283%2F3%29, typical fraction skill,

2x%2F%283%283x%2B5%29%29-8%2A3%2F%283%283x%2B5%29%29

%282x-24%29%2F%283%283x%2B5%29%29

highlight%28%282x-24%29%2F%289x%5E2%2B5%29%29----------this would be your finished form for #2.

Any restrictions on x?
Yes.
The denominator must be NONZERO.
9x%5E2%2B5%3C%3E0


Suggestion for #1 is to again, use the fraction skills which you already know. Your description of what you are starting with is %28%28x%5E2-x-6%29%2F%28x%5E2-4%29%29%2F%28%28x%5E2-2x%2B1%29%2F%28x%5E2-1%29%29.

What would you do for %28a%2Fb%29%28c%2Fd%29?
Then, what else to simplify, if possible?

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
I just posted this equation, but I don't think it was very clear soo hopefully this format clears up any confusion. I'm 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 2 examples I provided, I would really appreciate it. Thanks in advance!
They ask me to simplify and state the restrictions on the variable. (Dividing/Subtracting Rational Expressions)
1. The numerator consists of x^2 - x-6, and the denominator is x^2 -4. Then we have to DIVIDE that by the numerator which is x^2 -2x+1, divided by the denominator which is x^2-1.

2. The numerator consists of 2x, and is divided by 9x^2+15x. Then we have to SUBTRACT the numerator which is 8, by the denominator which is 3x+5.

I really hope this is clear. Im not sure how else to break it down since I have no idea how to type up equations. Thanks again!

1.
%28x%5E2+-+x+-+6%29%2F%28x%5E2+-+4%29%29%22%F7%22%28x%5E2+-+2x+%2B+1%29%2F%28x%5E2+-+1%29

%22%F7%22 ------ Factoring all numerators and denominators

%28x+-+3%29%28x+%2B+2%29%2F%28x+-+2%29%28x+%2B+2%29%22%F7%22%28x+-+1%29%28x+-+1%29%2F%28x+-+1%29%28x+%2B+1%29

%28x+-+3%29cross%28%28x+%2B+2%29%29%2F%28x+-+2%29cross%28%28x+%2B+2%29%29%22%F7%22cross%28%28x+-+1%29%29%28x+-+1%29%2Fcross%28%28x+-+1%29%29%28x+%2B+1%29 ------- Cancelling binomials to make process easier 

%28x+-+3%29%2F%28x+-+2%29%22%F7%22%28x+-+1%29%2F%28x+%2B+1%29

%28x+-+3%29%2F%28x+-+2%29%22%2A%22%28x+%2B+1%29%2F%28x+-+1%29 ------------ Keep, change, flip [Keep 1st fraction, change the division to multiplication, and then

                           INVERT (flip) fraction after division sign]

%28%28x+-+3%29%28x+%2B+1%29%29%2F%28%28x+-+2%29%28x+-+1%29%29, or highlight_green%28%28x%5E2+-+2x+-+3%29%2F%28x%5E2+-+3x+%2B+2%29%29

2.

2x%2F%289x%5E2+%2B+15x%29+-+8%2F%283x+%2B+5%29 

2x%2F3x%283x+%2B+5%29cross%28%289x%5E2+%2B+15x%29%29+-+8%2F%283x+%2B+5%29 ------ Factoring all numerators and denominators

2x%2F3x%283x+%2B+5%29+-+8%2F%283x+%2B+5%29 

2cross%28x%29%2F3cross%28x%29%283x+%2B+5%29+-+8%2F%283x+%2B+5%29 -------- Cancelling x in numerator and x in denominator 

2%2F3%283x+%2B+5%29+-+8%2F%283x+%2B+5%29

%282+-+8%283%29%29%2F3%283x+%2B+5%29 -------- Multiplying by LCD, 3(3x + 5)

%282+-+24%29%2F3%283x+%2B+5%29 

highlight_green%28%28-+22%29%2F3%283x+%2B+5%29%29 , or highlight_green%28%28-+22%29%2F%289x+%2B+15%29%29