Solve the following equation and explain each step used in solving the equation
(3 / (x -3)) = (1 / (x-1)) + (7 / ((x-1)(x-3))

Multiply all terms by (x-3)(x-1) would be your first step. 

This gives you:
3(x - 1) = (x - 3) + 7
3x - 3 = x + 4

-x on both sides:
2x - 3 = 4

Add 3 to both sides:
2x = 7

Divide both sides by 2:
x = 7/2

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