How do you solve #3/(x+6)=5/(x-2)# and find any extraneous solutions?

1 Answer
Dec 6, 2017

Answer:

#x=-18#

Explanation:

#"multiply both sides by "(x+6)(x-2)#

#cancel((x+6))(x-2)xx3/cancel((x+6))=cancel((x-2))(x+6)xx5/cancel((x-2))#

#rArr3(x-2)=5(x+6)larrcolor(blue)"no fractions"#

#"distribute brackets on both sides"#

#3x-6=5x+30#

#"subtract 5x from both sides"#

#3x-5x-6=cancel(5x)cancel(-5x)+30#

#rArr-2x-6=30#

#"add 6 to both sides"#

#-2xcancel(-6)cancel(+6)=30+6#

#rArr-2x=36#

#"divide both sides by "-2#

#(cancel(-2) x)/cancel(-2)=36/(-2)#

#rArrx=-18#

#color(blue)"As a check"#

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

#"left "=3/(-12)=-1/4#

#"right "=5/(-20)=-1/4#

#rArrx=-18" is the only solution"#