Thread: Need help with two rational expressions

1. Need help with two rational expressions

I'm having problems with two rational expressions that need to be worked out. I really need a step by step example so that I can do it on the test I'll be having soon.

is it $\displaystyle \frac {8(y - 4)}{20-y}$ with y not equal to -3 for the domain?

$\displaystyle \frac {4y - 16}{5y+15} * \frac {2y + 6}{4-y}$

and

$\displaystyle \frac {x - 13}{x^3(3 - x)} * \frac {x(x - 3)}{5}$

2. Originally Posted by Skynt

$\displaystyle \frac {x - 13}{x^3(3 - x)} * \frac {x(x - 3)}{5}$
$\displaystyle -\frac{(x-13)}{x^3(x-3)} \cdot \frac{x(x-3)}{5}$

$\displaystyle - \frac{(x-13)}{5x^2(x-3)}$

3. Originally Posted by Skynt
I'm having problems with two rational expressions that need to be worked out. I really need a step by step example so that I can do it on the test I'll be having soon.

$\displaystyle \frac {4y - 16}{5y+15} * \frac {2y + 6}{4-y}$
note that we can factor these:

$\displaystyle \frac {4y - 16}{5y+15} \cdot \frac {2y + 6}{4-y} = \frac {4(y - 4)}{5(y+3)} \cdot \frac {2(y + 3)}{4-y}$

can you continue?

and

$\displaystyle \frac {x - 13}{x^3(3 - x)} * \frac {x(x - 3)}{5}$
note that $\displaystyle \frac {x - 13}{x^3(3 - x)} \cdot \frac {x(x - 3)}{5} = \frac {x - 13}{x^3(3 - x)} \cdot \frac {-x(3 - x)}{5}$

can you continue?

4. I'm quite confused lol, can't you cancel out x-3 (sorry) and end up with
$\displaystyle \frac {-(x-13)}{5x^2}$ ?

5. Originally Posted by Skynt
I'm quite confused lol, can't you cancel out x-3 (sorry) and end up with
$\displaystyle \frac {-(x-13)}{5x^2}$ ?
yes, that is correct

Originally Posted by Skynt
I'm having problems with two rational expressions that need to be worked out. I really need a step by step example so that I can do it on the test I'll be having soon.

is it $\displaystyle \frac {8(y - 4)}{20-y}$ with y not equal to -3 for the domain?
no, it is for $\displaystyle y \ne 20$, since y = 20 is the problem spot here

6. Sorry for more questions, but I really need to grasp this completely. Thanks for the help so far, but what if I have:
$\displaystyle \frac {2x^2y}{xy - y}$ lost on this one.

7. Originally Posted by Skynt
Sorry for more questions, but I really need to grasp this completely. Thanks for the help so far, but what if I have:
$\displaystyle \frac {2x^2y}{xy - y}$ lost on this one.
$\displaystyle \frac{2x^2y}{y(x-1)} = \frac{2x^2}{x-1}$