Help!!

[Guest]

I have two problems that I need help with.

1. 4x^2 -1/ 4x+2

Find the exclusion
X does not equal _____

2. Reduce the algebraic fraction

a - a^4/a^2 + a + 1

a(____)

Fill in the blanks. I appreciate any help. :?

 

[pka]

Billy-0, your post is almost unreadable.
Please edit it. Add parentheses to group denominators.
You can type e^2 to mean e<SUP>2</SUP>.

 

[Guest]

I am really sorry about that. I didn't know how to type it correctly. Hopefully it is more readable now.

 

[soroban]

Hello, Billy-O!

I'll take a guess at what you meant . . .

\(\displaystyle 1)\;\;\frac{4x^2\,-\,1}{4x\,+\,2}\)

Find the exclusion: x does not equal _____ .

Since the denominator must not equal zero: \(\displaystyle \,4x\,+\,2\:\neq\:0\;\;\Rightarrow\;\;x\:\neq\:-\frac{1}{2}\)

2. Reduce the algebraic fraction: \(\displaystyle \frac{a\,-\,a^4}{a^2\,+\,a\,+\,1}\)

Factor: \(\displaystyle \L\:\frac{a(1 - a^3)}{1\,+\,a\,+\,a^2}\)

The numerator has a difference of cubes . . .

Factor: \(\displaystyle \L\:\frac{a(1\,-\,a)(\sout{1\,+\,a\,+\,a^2})}{\sout{1\,+\,a\,+\,a^2}} \;= \;a(1\,-\,a)\)

 

[Guest]

Thanks so much! That makes perfect sense and I don't know why I didn't think of that. Thanks again!!!