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Math Help - Help with Rational Expressions!

  1. #1
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    Help with Rational Expressions!

    I have a few problems i dont understand Please help they are the following,

    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!
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Lucster View Post
    I have a few problems i dont understand Please help they are the following,

    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?

    \frac{x+6}{4x}\leq\frac{x-3}{-4x-2}
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  3. #3
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    Yes it is except the 4x is -4x
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  4. #4
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    Anyone got a answer i really need this for tomorrow please? :]
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  5. #5
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Lucster View Post
    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 \frac{x-3}{-4x-2} from both sides.

    \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

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


    finding a common denominator we have

    \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 -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
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