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

Answer:

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

Step-by-step explanation:

Given:

The rational equation to solve is given as:

$\frac{x}{6}=\frac{x^2}{x-1}$

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

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

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

Also, $x=-\frac{1}{5}$ is also a solution as the equation's denominator is defined at that point.

So, no extraneous solution.