Question

Simplify
-14x^3/ x^3 - 5x^4

Answer 1

this is the same as the last question you asked. the steps are the same

Answer 2

would x not equai 1/5 and 0 or just 1/5 ?

Answer 3

you're trying to simplify yes? not solve for x

Answer 4

but i also need to find what x doesnt equal

Answer 5

what happens if x = 0?

Answer 6

then theres no solution

Answer 7

why is there no solution?

Answer 8

looks like there is a solution to me

Answer 9

then is it 0?

Answer 10

how does it show that it cant be 1/5?

Answer 11

because if x is 1/5, then the denominator would be 0... and we can't divide be 0

Answer 12

be careful when you simplify though, because when you bring out the x^3.. that actually does still exist. so x cannot be 0 either

Answer 13

oh. ok that makes sense x) i thought there was a special way to figure it out. not just plug it in

Answer 14

when we simplify, we are just reducing terms to make it easier to picture. but in this case we can factor out a x^3 from the top and bottom, which what really means is we multiply \[\frac{ 14 }{ 5x-1 }\]
by \[\frac{ x^3 }{ x^3}\]

which means x cannot be 0 either, because then 0 would be in the denominator of that fraction too

Answer 15

so if theres an x on the bottom it cant be zero or a number that cancels out the other number for it to be 0

Answer 16

got it :)

Answer 17

well not exactly in every case. in this example we factored out an x on the top and bottom. but lets say if we factored out

\[\frac{ x^3+1 }{ x^3+1 }\]
then x can still be 0

Answer 18

what i meant if its connected to another number

Answer 19

connect or not connect... coefficients shouldn't matter

Answer 20

ok