Question

How should I simplify this rational expression?

Answer 1

\[\frac{ 3a^3b^2 }{ 5a^4c^5 }\div \frac{ 12b^3c^3 }{ 20abc^4 }\]

Answer 2

the only thing i did so far was flip the 2nd question to multiply

Answer 3

\[\frac{ a^3 }{ a^4 }=\frac{ 1 }{ a }\]

Answer 4

i see that ^

Answer 5

\[\dfrac{b^3c^3}{bc^4}=\dfrac{b^2}{c}\]

Answer 6

i also see that

Answer 7

\[\frac{ 12 }{ 20 }=\frac{ 3\times 4 }{ 5\times 4 }\]

Answer 8

i should write it out like that?

Answer 9

4 will cutout

Answer 10

so for the first term is it \[\frac{ 3b^2 }{ 5ac^5 }\]

Answer 11

\[\Huge \checkmark\]

Answer 12

2nd term is \[\frac{ 3b^2 }{ 5ac }\]

Answer 13

?

Answer 14

now i flip the fraction to multiply?

Answer 15

yes

Answer 16

Flip over the second and combine the two, then simplify

Answer 17

so i can cross out the 3b^2

Answer 18

once i flip it

Answer 19

then i can make it 5ac/5ac^5 which is c^-4 or 1/c^4?

Answer 20

\[\frac{ 3*20*a^4*b^3*c^4 }{ 5*12*a^4*b^3*c^8 }\]

Answer 21

divide by 3 on top and bottom for 3/12 --> 1/4
Divide by 5 on top and bottom for 20/5 --->4/1

Answer 22

then they cancel, you have60/60 = 1

Answer 23

the a^4/a^4 cancels

Answer 24

and the b^3 cancels

then take away 4 from the c power

Answer 25

\[\frac{ 3b^2 }{ 5ac^5 }\times \frac{ 5ac }{ 3b^2 }\]

Answer 26

i crossed out the 3b^2 then subtracted c's

Answer 27

same result however

Answer 28

\[\frac{ 1 }{ c ^{8-4} }\]

Answer 29

right so yours is \[\frac{ 15 a* b^2 * c }{ 15 *a * b^2 * c^5 }\]

Answer 30

\[\frac{ c }{ c^5 } = \frac{ 1 }{ c ^{5-1} } = \frac{ 1 }{ c^4 }\]

Answer 31

yupp. got it. thanks again

Answer 32

welcome