Question

Need to know how to solve a rational equation

Answer 1

The following equation is one that I made up so I can solve the problem I have to do on my own.

Answer 2

this is the equation I made

Answer 3

I don't know why it came out like that

Answer 4

I would start like this:
\[(x^3-8x)^{-1}=\frac{x}x+\frac8x-6\]

Answer 5

okay hold on let me put the other equation in that form @agreene

Answer 6

Where did the ^-1 outside the first parenthesis come from? @agreene

Answer 7

its shorthand for the division

Answer 8

\[\frac1x=x^{-1}\]

Answer 9

so the ^-1 is coming from the 1 in the first part of the equation?

Answer 10

yes

Answer 11

okay so I put my equation in that form whats next?

Answer 12

you there? @agreene

Answer 13

what do I doo next?

Answer 14

lol im trying to remember.. im a bit rusty on the algebra here

Answer 15

haha its okay

Answer 16

\[\frac1{x^3-8x}=1+\frac8x-6\]
\[\frac1{x^3-8x}=\frac8x-5\]
\[\frac1{x^3-8x}-\frac8x=-5\]

Answer 17

The least common denominator is (x^3-8x).
Multiply throughout by (x^3-8x).
You will get a fourth degree polynomial which cannot be easily solved unless you use a graphic calculator.

Note that x cannot be 0 or \(\pm\sqrt{8}\) because that would make the denominator zero.

Answer 18

My equation was