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

Question

Isaiah Anthony · Accepted Answer

No solution

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 e 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

Eli Assouline · Answer

undefined To solve the equation (3x)/(x-5) = 5 - 5/(x-5) = 15, we can start by simplifying the equation. First, we can multiply both sides of the equation by (x-5) to eliminate the denominators. This gives us 3x = 5(x-5) - 5. Expanding the right side of the equation, we get 3x = 5x - 25 - 5. Simplifying further, we have 3x = 5x - 30. Next, we can subtract 5x from both sides of the equation to isolate the x term. This gives us -2x = -30. Finally, we can divide both sides of the equation by -2 to solve for x. This yields x = 15.