How do you solve #(3x)/(x-6)=5+18/(x-6)#?

2 Answers
Apr 14, 2018

Answer:

#x=6#

Explanation:

First make the five into a fraction and then add the two fractions together.

#(3x)/(x-6) = (5(x-6))/(x-6) + 18/(x-6)#

#(3x)/(x-6) = (5(x-6) +18)/(x-6)#

#(3x)/(x-6) = (5x -30 +18)/(x-6)#

#(3x)/(x-6) = (5x-12)/(x-6)#

Cross multiply to make a linear equation.

#3x(x-6) = (5x-12)(x-6)#

Cancel out the #(x-6)# on both sides and then simplify to solve for #x#.

#3x = 5x-12 -> 5x-3x =12#

#2x = 12#

#x=6#

Apr 14, 2018

Answer:

#x=6#

Explanation:

Solve:

#(3x)/(x-6)=5+(18)/(x-6)#

Multiply both sides by the least common denominator #(x-6)#.

#color(red)cancel(color(black)((x-6)))xx(3x)/color(red)cancel(color(black)((x-6)))=5(x-6)+18/color(red)cancel(color(black)((x-6)))xxcolor(red)cancel(color(black)((x-6)))#

Simplify.

#3x=5(x-6)+18#

Expand.

#3x=5x-30+18#

Simplify.

#3x=5x-12#

Subtract #5x# from both sides.

#3x-5x=-12#

Simplify.

#-2x=-12#

Divide both sides by #-2#.

#(color(red)cancel(color(black)(-2))^1x)/(color(red)cancel(color(black)(-2)))^1=(color(red)cancel(color(black)(-12)))^(6)/color(red)cancel(color(black)((-2)))^1# #larr# Two negatives make a positive.

Simplify.

#x=6#