Question

What is the simplified form of the rational expression.

Answer 1

6x^2-54/5x^2+15x

Answer 2

are you asking this?
\[\frac{6x^3-54}{5x^2+15x}\]

Answer 3

6x^2 on that.

Answer 4

yes exactly

Answer 5

yea with 6x^2 instead of 6x^3

Answer 6

factoring would be a good start. Try factoring the numerator and denominator.

Answer 7

ok so for which number?

Answer 8

you can factor the top and the bottom, think of values you can pull out for each one

Answer 9

o i get it srry

Answer 10

(6x+9)(x-6)

Answer 11

the numerator would be done as such:
\[6x^2-54 \rightarrow 6(x-3)(x+3)\]

Answer 12

can you please show me how

Answer 13

ohhhh

Answer 14

ok so 6*x would be 6x and x would be 6x^2 and 6*3 would be 18 and times 3 would be -54

Answer 15

\(6x^2-54\) pull 6 out for each \(6(x^2-9)\) divide parenthetical statement \(6(x-3)(x+3\)

Answer 16

right

Answer 17

now try the denominator

Answer 18

5(x+5)(x+3)?

Answer 19

taking out 5x would be more effective

Answer 20

since 15x is divisible

Answer 21

oh ok

Answer 22

\[5x^2+15x \rightarrow 5x(x-3)\]

Answer 23

so, then we would combine them:
\[\frac{6(x-3)(x+3)}{5x(x-3)}\]

Answer 24

o so you cross out (x-3) and (x-3) and 6(x+3)/5x is the answer!

Answer 25

that can be the answer, technically you can simplify it a bit more. But that should be fine.

Answer 26

um i got it wrong :(

Answer 27

it was 6(x-3)/5x

Answer 28

yeah

Answer 29

i put the wrong sign on the 2nd factor. thats mah bad

Answer 30

5x^2+15 -> 5x(x+3)