Question

How do you solve `x/(x^2-8)=2/x`?

Answer 1

`x=+-4`

Explanation:

First, move everything from the denominator to the numerator
we do this by multiplying by the LCM of denominators on each side.

`x(x^2-8)* x/(x^2-8)= 2/x *x(x^2-8)`

the `(x^2-8)` on the left side cancels out and the `x` on the right side cancels out

`x(cancel(x^2-8))* x/(cancel(x^2-8))= 2/cancelx *cancelx(x^2-8)`

which leaves us with:

`x*x=2*(x^2-8)`

after this we now have
`x^2=2(x^2-8)`

next we remove the parentheses by multiplying each term by 2
now we have
`x^2=2x^2-16`

next we will move the 16 to the other side to avoid working with negative numbers
`16+x^2=2x^2`

then we will combine like terms by subtracting `x^2`
`16=2x^2-x^2` leaving us with `16=x^2`

then we will get rid of the `x^2` by taking the square root of both sides
`+-sqrt16`=`sqrtx^2`

now we have our final answer of
`x=+-4`