How do you solve #3/(x+6)=5/(x-2)# and find any extraneous solutions?
1 Answer
Dec 6, 2017
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"#