Question

hi can anyone help me with this problem?
(a^2+5a+4/a^3)/(a^2+3a+2/a^2-2a)
please show your work so i know what youre doing,,

Answer 1

if it helps written out it would be

\[\frac{ a ^{2} + 5a+4 }{ a ^{3} } \div \frac{ a ^{2}+3a+2 }{ a ^{2}-2a }\]

Answer 2

do you know how to factor any of the expressions here?

Answer 3

multiply by the reciprocal and factor

Answer 4

how would i factor them

Answer 5

$$\frac{ a ^{2} + 5a+4 }{ a ^{3} } \div \frac{ a ^{2}+3a+2 }{ a ^{2}-2a }
\\~\\ =\frac{ (a+1)(a+4)}{ a ^{3} } \div \frac{ (a+1)(a+2) }{a(a-2) }
\\~\\ =\frac{ (a+1)(a+4)}{ a ^{3} } \cdot \frac{ a(a-2) }{ (a+1)(a+2) }

$$

Answer 6

thanks, would I subtract out the a+1 ? or no

Answer 7

yes, cancel out

Answer 8

could I also cancel out the a on the numerator and denominator of the second fraction?

Answer 9

yes :)

Answer 10

is this right
\[\frac{ a+4 }{ a ^{3} } \div \frac{ a-2 }{ 2 }\]

Answer 11

shouldn't be a division sign

Answer 12

oh right sorry i knew that

Answer 13

but is that right

Answer 14

$$


\frac{ a ^{2} + 5a+4 }{ a ^{3} } \div \frac{ a ^{2}+3a+2 }{ a ^{2}-2a }
\\~\\ =\frac{ (a+1)(a+4)}{ a ^{3} } \div \frac{ (a+1)(a+2) }{a(a-2) }
\\~\\ =\frac{ (a+1)(a+4)}{ a ^{3} } \cdot \frac{ a(a-2) }{ (a+1)(a+2) }
\\~\\ =\frac{\cancel{ (a+1)}(a+4)}{ \cancel{a ^3} } \cdot \frac{ \cancel{a}(a-2) }{\cancel{(a+1)}(a+2) }
\\~\\ =\frac{ (a+4)}{ a ^2 } \cdot \frac{ (a-2) }{ (a+2) }

\\~\\ =\frac{ (a+4)(a-2)}{ a ^2(a+2) }
$$

Answer 15

and would the answer be

\[\frac{ (a+4)(a-2) }{ a ^{2}(a+2) }\]

Answer 16

I went with that and that was the right answer :)