Question

(x)/(x-2) - (x+1)/(x) = (8)/(x^2-2x)

I keep getting x = 6

can someone show me how you guys are getting x = -10



The lowest commond denominator is x(x-2)

x/x *(x)/(x-2) - (x+1)/(x) *(x-2)/(x-2)=(8)/x(x-2)

multiplying both sides by the common denominator..

x^2 -(x^2-1x -2)=8
x+2=8
x=6

check
6/4 - 7/6=8/24
36/24 - 28/24=
8/24=8/24
it checks.



OK, here's how I would go about this problem:

(x)/(x-2) - (x+1)/(x) = (8)/(x^2-2x)

(x)/(x-2) - (x+1)/(x) = (8)/x(x-2) -->factoring the denominator (x^2-2x).

Common denominator is: x(x-2)

Multiply every term by the common denominator to get rid of the fractions and make the equation easier to solve.

x(x-2) [(x)/(x-2) - (x+1)/(x) = (8)/x(x-2)]

x^2 - (x+1)(x-2) = 8

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

x^2 - x^2 + x + 2 = 8

x + 2 = 8

x = 6

Substitute 6 for x in the original equation. It always helps to check your work!

I hope this is clear and will help.

you get the same answer as i do but others are saying here someone named annonimous that they keep getting -10.