Question

How do you solve `(40/(x-2))=1+(42/(x- 2))`?

Answer 1

`x=0`

Explanation:

Given,

`40/(x-2)=1+42/(x-2)`

Multiply each term on the left and right sides by `x-2` to get rid of the denominators.

`color(red)((x-2))(40/(x-2))=1color(red)((x-2))+color(red)((x-2))(42/(x-2))`

Simplify.

`(color(red)cancelcolor(black)(x-2))(40/(color(red)cancelcolor(black)(x-2)))=1(x-2)+(color(red)cancelcolor(black)(x-2))(42/(color(red)cancelcolor(black)(x-2)))`

`40=x-2+42`

`40=x+40`

Subtract `40` from both sides.

`40color(white)(i)color(red)(-40)=x+40color(white)(i)color(red)(-40)`

`x=color(green)(|bar(ul(color(white)(a/a)color(black)0color(white)(a/a)|)))`