# Math Help - rational functions

1. ## rational functions

x+3/(x+6)(x+4) + 5/4-x=x+2/3-x

this is what I have done so far...

I know to put a negative 1 from the 4-x and the 3-x in order to get -1(x-4) and -1(x-3)

Now I have -1(x+3)(x-3) this is where I am stuck at..if someone could
(x+6)(x-4)

please walk me through this step by step, I would greatly appreciate it.

2. Originally Posted by getnaphd
x+3/(x+6)(x+4) + 5/4-x=x+2/3-x

this is what I have done so far...

I know to put a negative 1 from the 4-x and the 3-x in order to get -1(x-4) and -1(x-3)

Now I have -1(x+3)(x-3) this is where I am stuck at..if someone could
(x+6)(x-4)

please walk me through this step by step, I would greatly appreciate it.
please use parentheses. is the equation $\frac {x + 3}{(x + 6)(x + 4)} + \frac {5}{4 - x} = \frac {x + 2}{3 - x}$ ?

what exactly are we supposed to do? solve for x? prove one side is equivalent to the other?

3. ## rational functions

Yes this is exactly what the equation looks like.

It says solve the equation.

4. ## rational functions

I don't know where to go once the -1 is removed from the fraction in the denominator.

5. Originally Posted by getnaphd
I don't know where to go once the -1 is removed from the fraction in the denominator.
please double check the question. the problem boils down to solving a quartic equation which has no nice solutions. it would not be reasonable to ask you to solve such a question without technology

6. Originally Posted by getnaphd
I don't know where to go once the -1 is removed from the fraction in the denominator.
$\frac{a}{-b} = \frac{-a}{b} = -\frac{a}{b}$

So:
$\frac {x + 3}{(x + 6)(x + 4)} + \frac {5}{4 - x} = \frac {x + 2}{3 - x}$ <-- Factor a -1 from the 4 - x and the 3 - x terms

$\frac {x + 3}{(x + 6)(x + 4)} + \frac {5}{-(x - 4)} = \frac {x + 2}{-(x - 3)}$ <-- The -1 factor changes the sign of the whole term

$\frac {x + 3}{(x + 6)(x + 4)} + -\left ( \frac {5}{x - 4} \right ) = - \left ( \frac {x + 2}{x - 3} \right )$

$\frac {x + 3}{(x + 6)(x + 4)} - \frac {5}{x - 4} = - \frac {x + 2}{x - 3}$

You can take it from here. But Jhevon is right, this one's a monster without numerical approximation.

-Dan