im not sure how to simplify: a^3+1/6a^2 X 3a/a^2+a

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im not sure how to simplify: a^3+1/6a^2 X 3a/a^2+a

Mathematics
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someone please please please help me i'm not too good with factorising and simplifying, no matter how basic those skills are D:
\[a ^{3}/1+ (1/6)*/(a^2)/1+(3/1)*a/a^2+a/1\] Create full fractions of each term. Next factor the top and bottom of each term separately. So a^2/1 becomes (a*a)/1. Finally determine if any factor (whether a variable or numeral) appears in all the terms. You should find that only (a/1) is able to factor out. [Corrections welcome.]
thanks but i dont think i wrote the question properly D: sorry its umm simplify a^3+1 3a ________ X ________ 6a^2 a^2+a sorry for the inconvenience. and if its the same thing just call me stupid :)

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Other answers:

\[((a^3 +1)/6a^2)*(3a/(a^+a)) = (3*(a^3+1))/(6^a^2(a+1))=(3a^3+3)/(6a^3+6)=1/2*(a^3+1)\] i think this is the ans. go each step by urself to understand it.
\frac{{\mathrm{(}}{a}^{3}\mathrm{{+}}{1}{\mathrm{)(}}{3}{\mathrm{)(}}{a}{\mathrm{)}}}{{\mathrm{(}}{3}{\mathrm{)(}}{2}{\mathrm{)(}}{a}{\mathrm{)(}}{a}{\mathrm{)[}}{a}{\mathrm{(}}{a}\mathrm{{+}}{1}{\mathrm{)]}}}\mathrm{{=}}\frac{{3}{a}{\mathrm{[(}}{a}^{3}\mathrm{{+}}{1}{\mathrm{)]}}}{{3}{a}{\mathrm{(}}{2}{a}{\mathrm{)(}}{a}^{2}\mathrm{{+}}{a}{\mathrm{)}}}
\[{{(a^{3}+1)(3)(a)}\over{(3)(2)(a)(a)[a(a+1)]}}={{3a[(a^{3}+1)]}\over{3a(2a)(a^{2}+a)}}\] Blah -trying to learn to post in TeX.
Ok - canceling the common term 3a top and bottom - the remultiplying, I get: \[{{[(a^{3}+1)]}\over{(2a^{3}+2a^{2})}}\] ... if I've read your equation correctly.
moss's bro you are entirely right! i made a mistake with typing on the TeX the last step you can also put like \[1/2 * ([a^3+1]/[a^3+a^2])\]
Cool. BTW, I'm using two helper programs to cut and paste proper TeX equations. One is a visual editor (MathMagic) - useful.
D: i don't know where i went wrong my answer ended up being \[a^{2}-a+1\] ______________ \[2a ^{2}\] any ideas on what im doing wrong?
No I can't really see how you got the trinomial on the top. Can you post your intermediate steps? BTW type "\frac{a+b){a^2} in the Equation editor to compose the fraction a+b)/a^2 for example.

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