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