Can someone help me reduce this? I have no idea what to do with the denominator. :-(

$\displaystyle \frac{4x^4-25}{6x^3-4x^2+15x-10}$

Thank you very much!

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- Jun 6th 2010, 04:22 PMyvonnehrreduce to lowest terms - fraction of polynomials
Can someone help me reduce this? I have no idea what to do with the denominator. :-(

$\displaystyle \frac{4x^4-25}{6x^3-4x^2+15x-10}$

Thank you very much! - Jun 6th 2010, 04:28 PMharish21
Numerator : $\displaystyle {4x^4-25} = (2x)^2-(5)^2 $

Since $\displaystyle a^2-b^2=(a+b)(a-b)$ , you can write

$\displaystyle {4x^4-25}= (2x+5)(2x-5)$

and you have:

Denominator: $\displaystyle 6x^3-4x^2+15x-10 = 2x^2(3x-2)+5(3x-2) = (3x-2)(2x^2+5)$

so you have:

$\displaystyle \frac{4x^4-25}{6x^3-4x^2+15x-10}$ $\displaystyle = \frac{(2x+5)(2x-5)}{(3x-2)(2x^2+5)}$

cancel out the like terms - Jun 6th 2010, 04:29 PMTheEmptySet
- Jun 6th 2010, 04:42 PMyvonnehrMany Thanks!
Many Thanks, Gentlemen!