# Fraction Equalities

• Oct 20th 2009, 06:48 PM
nmbala
Fraction Equalities
I am working on a class project on the derivation of the quadratic formula, and i understand the process of completing the square, up until the very last process of simplifying back to the quadratic forumla...

Can someone explain how
$
-\frac{c}{a} + \frac{b^2}{4a^2} = \frac{b^2 - 4ac}{4a^2}
$
• Oct 20th 2009, 06:56 PM
ramiee2010
Quote:

Originally Posted by nmbala
I am working on a class project on the derivation of the quadratic formula, and i understand the process of completing the square, up until the very last process of simplifying back to the quadratic forumla...

Can someone explain how -c/a + b^2/4a^2 = (b^2 - 4ac)/4a^2

it is just basic operation on fractions
$\frac{-c}{a} + \frac{b^2}{4a^2}$
LCM of a and $4a^2$ is $4a^2$
$\frac{-c}{a}+ \frac{b^2}{4a^2} =\frac{{-c}\times (4a)+b^2\times 1}{4a^2} = \frac{-4ac+b^2}{4a^2}= \frac{b^2-4ac}{4a^2}$

or you can understand it as
multiply numerator &denominator of $\frac{-c}{a}$ by 4a

${\color {blue}\frac{-c}{a}}+ \frac{b^2}{4a^2} ={\color {blue}\frac{-4ac}{4a^2}}+ \frac{b^2}{4a^2} = \frac{-4ac+b^2}{4a^2}= \frac{b^2-4ac}{4a^2}$
• Oct 20th 2009, 07:04 PM
nmbala
Quote:

Originally Posted by ramiee2010
it is just basic operation on fractions
$\frac{-c}{a} + \frac{b^2}{4a^2}$
LCM of a and $4a^2$ is $4a^2$
$\frac{-c}{a}+ \frac{b^2}{4a^2} =\frac{{-c}\times (4a)+b^2\times 1}{4a^2} = \frac{-4ac+b^2}{4a^2}= \frac{b^2-4ac}{4a^2}$

Wow ok thx.. been a few years since ive taken a math course appears ive forgotten some of my basics of adding/subtracting fractions... Thx a bunch