Question

Solve rational equation:

Answer 1

\[\frac{ 2x }{ 2x-3 }+ \frac{ 4 }{ x }=\frac{ x-18 }{ x(2x-3) }\]

Answer 2

@jim_thompson5910 this is my last one and I am out of hear for the night

Answer 3

First you have to identify the LCD and make the other terms simmilar!

Answer 4

(2x)/(2x-3) + 4/x = (x-18)/(x(2x-3))
2x + (2x-3)(4)/x = (x-18)/x
2x^2 + 8x - 12 = x -18
2x^2 + 7x + 6 = 0
2x^2 + 4x + 3x + 6 = 0
2x(x + 2) + 3(x+2) = 0
(2x + 3)(x + 2) = 0
2x + 3 = 0 and x + 2 = 0
2x = -3 and x = -2
x = -3/2

Answer 5

@franciscanmonk is the reason you didn't use 2x-3 because -3 is the restriction

Answer 6

no. i used (2x - 3)
it disappeared after line 4 of my solution.
i distributed it and then the -18 got transferred and so...the solution goes.

Answer 7

^ what does that mean

Answer 8

(2x)/(2x-3) + 4/x = (x-18)/(x(2x-3))
I distribiuted (2x-3) and thus it is gone in the 2nd line.. i 2x-3 is gone from the denominator of the 1st one and the 3rd one.
2x + (2x-3)(4)/x = (x-18)/x
I distributed x so that it will vanish from the denominators of the others.
2x^2 + 8x - 12 = x -18 <--- I distributed (2x-3) and got 8x-12

there is no restriction here.