5/x-1=4/x+1/2x?

Hi,

5........4......1
---- = ---- + ----
x-1.... x...... 2x

Multiply every term by 2x(x - 1) to eliminate the fractions.

5(2x) = 4(2)(x - 1) + 1(x - 1)

10x = 8x - 8 + x - 1

10x = 9x - 9

x = -9 <==ANSWER

I hope that helps!! :-)

Hopefully you mean :-
5 / (x - 1) = (4 / x) + 1 / (2x)
5 (x)( 2x) = 4 (x - 1) (2x) + (x - 1) (x)
10x² = 8x² - 8x + x² - x
x² + 9 x = 0
x (x + 9) = 0
x = 0 , x = - 9

5/(x - 1) = 4/x + 1/2x
2x[x - 1][5/(x - 1)] = 2x[x - 1][4/x + 1/2x]
5[2x] = 8[x - 1] + [x - 1]
10x = 8*x - 8*1 + x - 1
10x = 8x - 8 + x - 1
10x - 8x - x = -8 - 1
x = -9

5/x=4/x+1/2x+1
5/x-4/x-0.5/x=1
(5-4-0.5)/x=1
(1-0.5)/x=1
0.5/x=1
0.5=1x
x=0.5