# Confused on how a complex polynomial fractions are simplified in sample problems

• Mar 1st 2013, 10:06 AM
melbell
Confused on how a complex polynomial fractions are simplified in sample problems
I am taking an intermediate algebra course and am stumped on one topic. We are doing complex polynomial fractions and I can figure out how they are simplifying one type of problem. Here is an example:

7 14
___ - ____ 7x2 -14x 7x
x x2 ___________________ ____________
_________________________ I keep coming up with but am told the answer is simplified to
4 16 4x2 -16 4(x+2)
____ - ____
x x3

Please help me understand how this is being simplified. THANKS!!!!
• Mar 1st 2013, 10:10 AM
melbell
Re: Confused on how a complex polynomial fractions are simplified in sample problems
erg. it formatted that weirdly.
7x*squared* - 14x
________________
4x*squared* -1

is being reduced to:

7x
______
4(x+2)
• Mar 1st 2013, 02:57 PM
Prove It
Re: Confused on how a complex polynomial fractions are simplified in sample problems
Quote:

Originally Posted by melbell
erg. it formatted that weirdly.
7x*squared* - 14x
________________
4x*squared* -1

is being reduced to:

7x
______
4(x+2)

Factorise the top and bottom, then cancel any common factors between them.

\displaystyle \begin{align*} \frac{7x^2 - 14x}{4x^2 - 1} &= \frac{7x \left( x - 2 \right)}{\left( 2x - 1 \right) \left( 2x + 1 \right) } \end{align*}

There are not any common factors, so either you have copied the question down wrong, or your book's answer is wrong.
• Mar 1st 2013, 03:24 PM
Soroban
Re: Confused on how a complex polynomial fractions are simplified in sample problems
Hello, melbell!

Quote:

$\text{Simplify: }\:\dfrac{\dfrac{7}{x} - \dfrac{14}{x^2}}{\dfrac{4}{x} - \dfrac{16}{x^3}}$

Multiply by $\frac{x^3}{x^3}\!:\;\;\frac{x^3\left(\dfrac{7}{x} - \dfrac{14}{x^2}\right)}{x^3\left(\dfrac{4}{x} - \dfrac{16}{x^3}\right)} \;=\;\frac{7x^2-14x}{4x^2-16}$

. . . . . . . . . . $=\;\frac{7x(x-2)}{4(x^2-4)} \;=\;\frac{7x(x-2)}{4(x-2)(x+2)} \;=\;\frac{7x}{4(x+2)}$