Question

Solve the rational equation x divided by 6 equals x squared divided by quantity x minus 1 end quantity, and check for extraneous solutions.

x = negative one fifth; 0 is an extraneous solution
x = 0; x= negative one fifth is an extraneous solution
No solution
x = 0 and x = negative one fifth

Answer 1

in other words, D

Answer 2

`x = 0` and
`x = \textrm{negative one fifth}`

Explanation:

Given:

The rational equation to solve is given as:

`(x)/(6)=(x^2)/(x-1)`

We use the cross multiplication rule and multiply the numerators one side with the denominators of the other side. Therefore,

`x* (x-1)=6* x^2\\x^2-x=6x^2\\\textrm{Bringing all variables to the right side, we get:}\\6x^2-x^2+x=0\\5x^2+x=0\\x(5x+1)=0\\x=0\ or\ 5x+1=0\\x=0\ or\ x=-(1)/(5)`

Now, for
`x=0`, the rational equation is equal to 0. So,
`x=0` is a solution.

Also,
`x=-(1)/(5)` is also a solution as the equation's denominator is defined at that point.

So, no extraneous solution.