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

___ - ____ 7x^{2} -14x 7x

x x^{2 }___________________ ____________

_________________________ I keep coming up with but am told the answer is simplified to

4 16 4x^{2} -16 4(x+2)

____ - ____

x x^{3}

Please help me understand how this is being simplified. THANKS!!!!

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)

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.

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

There are not any common factors, so either you have copied the question down wrong, or your book's answer is wrong.

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

Hello, melbell!

Quote:

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

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

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