Question

How do you solve `(3x)/(x+1)+6/(2x)=7/x`?

Answer 1

`x=-2/3` or `x=2`

Explanation:

`(3x)/(x+1)+6/(2x)=7/x` can be rewritten as

`(3x)/(x+1)=7/x-6/(2x)`

or `(3x)/(x+1)=7/x-3/x=4/x`

Hence, `(3x)/((x+1))xx x(x+1)=4/x xx x(x+1)`

or `(3x)/(cancel(x+1))xx xcancel((x+1))=4/cancelx xx cancelx(x+1)`

or `3x^2=4x+4`

or `3x^2-4x-4=0`

or `3x^2-6x+2x-4=0`

or `3x(x-2)+2(x-2)=0`

or `(3x+2)(x-2)=0`

Hence either `3x+2=0` i.e. `x=-2/3`

or `x-2=0` i.e. `x=2`