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

1 Answer
Jul 27, 2016

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