solve for x

[krisolaw]

1/x - 1/y + 1/z = 5

I know I need to multiply by the LCD, but factoring out the x has become troublesome. Please help ASAP! Thanks!

 

[arthur ohlsten]

1/x + 1/y + 1/z =5

denominator 1 =x
denominator 2 =y
denominator 3 =y
------------------------
lowest common denominator[lcd]=xyz
multiply left side by xyz/xyz where no term is 0
xyz/[[x][xyz]] + xyz/[y[xyz]]+xyz/[z[xyz]] = 5 simplify
yz/xyz + xz/xyz + xy/xyz =5 place over common denominator xyz
[yz+xz+xy] / xyz =5 multiply both sides by xyz
yz+ xz+ xy= 5 xyz place all x terms on left and other terms on right
xz+xy -5xyz= -yz factor out x
x[z+y-5yz]= -yz
x= -yz/[y+z-5yz] answer multiply by -1/-1
x=yz/[5yz-y+z] answer
Arthur
plewase check for errors

 

[soroban]

Hello, krisolaw!

1/x - 1/y + 1/z = 5
I know I need to multiply by the LCD, but factoring out the x has become troublesome.

After multiplying by the LCD (xyz), you should have:

. . . yz - xz + xy . = . 5xyz


Get all the x-terms on one side:

. . . xy - xz - 5xyz . = . yz


Factor out the x:

. . . x(y - z - 5yz) . = . yz


Finally:
. . . . . . . . . . . .yz
. . . x . = . --------------
. . . . . . . . .y - z - 5yz