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Simplify the following:?

(6x^2 + 3x)/4x^2 - 1

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    The first thing you need to do, before simplifying, is factor out the numerator and denominator.

    3x(2x + 1) <-- Factor out the (3x) which is the GCF

    ---------------

    (2x - 1)(2x + 1)

    I think it is worth mentioning that although there is nothing to factor out in the denominator, it is called the difference of two squares. This means that if the problem fits this format (a^2 - b^2), then its factored form is (a - b)(a + b).

    Now that it is factored you can see that the (2x + 1)'s cancel out. This leaves you:

    3x

    -----

    (2x - 1)

    It cannot be simplifying further, so you're done!

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