Question

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

Answer 1

`x=-5`

Explanation:

`"one way is to use the method of "color(blue)"cross-multiplication"`

`"given " a/b=c/d" then " ad=bc`

`"applying this to the equation"`

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

`6x+12=3x-3larr" distributing"`

`"subtract 3x from both sides"`

`6x-3x+12=cancel(3x)cancel(-3x)-3`

`rArr3x+12=-3`

`"subtract 12 from both sides"`

`3xcancel(+12)cancel(-12)=-3-12`

`rArr3x=-15`

`"divide both sides by 3"`

`(cancel(3) x)/cancel(3)=(-15)/3`

`rArrx=-5`

`color(blue)"As a check"`

Substitute this value into the equation and if both sides are equal then it is the solution.

`"left side "=3/(-5+2)=3/(-3)=-1`

`"right side " =6/(-5-1)=6/(-6)=-1`

`rArrx=-5" is the solution"`