Solve the equation. (x – 3)/(3) = (x + 5)/(7)?

7x - 21 = 3x + 15
4x = 36
x = 9

(x - 3)/3 = (x + 5)/7
7(x - 3) = 3(x + 5)
7x - 21 = 3x + 15
4x = 36
x = 9

Answer: x = 9

Proof:
(9 - 3)/3 = (9 + 5)/7
6/3 = 14/7
2 = 2

I am sometimes thinking that some mad, crazy and innecessary guy writes a question and waits people to solve the problem and as they are doing that he is sickly laughing on his chair. I just can't help it.

First of all, I chose to clear out the fractions by multiplying both sides by 21.
(21)* (X -3)/3 = (21)* (X + 5)/7
this gives
7 ( X-3) = 3 (X + 5)
Multiplying through by way of the distributive law,
you get
7X - 21 =3X + 15
Bringing the 3X over onto the left side, and the - 21 over to the right, so that you have all X terms on the left and all numbers on the right, you end up with:
4X = 36.
Dividing both sides by 4,
you get
X =9.
Check by substituting 9 in place of x in the original equation,you get (9-3)/3, which equals 6/3 which equals 2.
And (9+5)/7 = 14/7 which also equals 2.
2=2 obviously,
and you can consider the equation solved.

(X - 3)/(3) = (X + 5)/7
(X - 3)(7) = (X + 5)(3)
7X - 21 = 3X + 15
7X - 3X = 15 + 21
4X = 36
X = 36/4
X = 9

(x-3)/3 = (x+5)/7
7x-21=3x+15
4x = 36
x=9

7(x - 3) = 3(x + 5)
7x - 21 = 3x + 15
4x = 36
x = 9

Multiply both sides by LCD 21
7(x - 3) = 3(x+5)
Simplify
7x - 21 = 3x + 15
4x = 36
x = 9

x = 9

(x - 3)/3 = (x + 5)/7
(7x - 21)/21 = (3x + 15)/21
7x - 21 = 3x + 15
7x - 3x = 21 + 15
4x = 36
x = 36/4
x = 9