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

1 Answer
May 17, 2017

Answer:

#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"#