Question

solve for
10/x^2-2x + 4/x = 5/x-2


3x/x+1 + 6/2x = 7/x


8(x-1)/x^2-4 = 4/x-2

check for any extraneous solutions! thanks!

Answer 1

I'll do one, and you try the others. If you get stuck, come on back.

10/(x^2-2x) + 4/x = 5/(x-2)

x^2-2x = x(x-2), so that's the LCD. Multiply through to get

10 + 4(x-2) = 5x
10 + 4x - 8 = 5x
x = 2
Unfortunately, the original equation has (x-2) in the denominator, so it is undefined there. No solution.