# Thread: Help with Rational Expressions!

1. ## Help with Rational Expressions!

x+6/-4x <= x-3/-4x-2

x+1/-3x => x-5/-3x+3

x-3/-x => x+4 / -x-1

=> means greater than or equal too
<= means less than or equal too

im decently good at math just need to refresh my memory please help with work so that i can understand and private message me when i get a response so i can check it more quickly thanks!

2. Originally Posted by Lucster

x+6/-4x <= x-3/-4x-2

x+1/-3x => x-5/-3x+3

x-3/-x => x+4 / -x-1

=> means greater than or equal too
<= means less than or equal too

im decently good at math just need to refresh my memory please help with work so that i can understand and private message me when i get a response so i can check it more quickly thanks!
I'm not sure what you are saying. Is this the first problem?

$\displaystyle \frac{x+6}{4x}\leq\frac{x-3}{-4x-2}$

3. Yes it is except the 4x is -4x

4. Anyone got a answer i really need this for tomorrow please? :]

5. Originally Posted by Lucster
Yes it is except the 4x is -4x
Okie Dokie. First hting we do is recognize that if we were to cross multiply, we would have to consider when the for what intervals of x would make the denomiators equal to 0. But let's not worry about that because it makes our job harder than it has to be. Instead, let's start by subtracting $\displaystyle \frac{x-3}{-4x-2}$ from both sides.

$\displaystyle \frac{x+6}{-4x}-\frac{x-3}{-4x-2}\leq0$

just to make it more visually appealing let's factor out a -1 from the right hand term

$\displaystyle \frac{x+6}{-4x}-\frac{3-x}{4x+2}\leq0$

finding a common denominator we have

$\displaystyle \frac{(4x+2)(x+6)-(-4x)(3-x)}{-4x(4x+2)}\leq0$

now you can see that the numerator must be equal to or less than 0 for the thing to be valid. So we can just multiply bot sides of the inequality by $\displaystyle -4x(4x+2)$. but we have to be care ful here because we know that if we multiply both sides by a negative number we must reverse the sign of the inequality. So, we must find the values of x that would make the denominator < 0. Is that a good head start for you?

Here's a place where you can refresh:
Algebra Help - Polynomial and Rational Inequalities