# reduce to lowest terms - fraction of polynomials

• Jun 6th 2010, 04:22 PM
yvonnehr
reduce 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 PM
harish21
Quote:

Originally Posted by yvonnehr
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!

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 PM
TheEmptySet
Quote:

Originally Posted by yvonnehr
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!

The denominator can be factored by grouping

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

Can you finish from here?

Too slow
• Jun 6th 2010, 04:42 PM
yvonnehr
Many Thanks!
Many Thanks, Gentlemen!