How do you solve #(3x)/( x-5) = 5 - 5 / (x-5)=15#?

1 Answer

Answer:

No solution

Explanation:

Given equality:

#\frac{3x}{x-5}=5-\frac{5}{x-5}=15#

#\frac{3x}{x-5}=\frac{5x-30}{x-5}=15#

1) Consider

#\frac{3x}{x-5}=\frac{5x-30}{x-5}#

#\frac{3x}{x-5}-\frac{5x-30}{x-5}=0#

#\frac{3x-5x+30}{x-5}=0#

#\frac{-2x+30}{x-5}=0#

#-2x+30=0\ \quad (\forall \ x\ne 5)#

#2x=30#

#x=15#

2) Consider

#\frac{3x}{x-5}=15#

#x=5(x-5)#

#4x=25#

#x=25/4#

#x=6.25#

3) Consider

#\frac{5x-30}{x-5}=15#

#5x-30=15(x-5)#

#10x=45#

#x=4.5#

Since, the values of #x# in all three cases are different hence the given equality doesn't have any solution