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Make Lemonade out of lemons: Subtraction to addition

Life is rife with "negatives" and so is mathematics. In this case a negative is a subtraction problem. When we deal with larger problems, we can get bogged down and forget that we are subtracting all terms within a parenthesis. My solution a three step revolution:

1) Bracket all terms
2) Turn a negative into a positive (a subtraction problem into an addition problem)
3) Solve

Such distribution errors are commonly seen in rational functions which require finding a common denominator; let's see an example below:

2x - 3
___ ___ = 5
(x+1) x

Now the common denominator is x(x+1), but if we fail to use brackets and distribute, we will get the wrong answer. Let's use the substitution revolution:

1) Bracket all terms
2x(x)/ x(x+1) -3(x+1)/x(x+1) =5

This makes sure we distribute the second numerator to x and 1

2) Turn the negative to a positive: this means that we want to turn the subtraction problem to an addition problem. we will do this by making -3 into + -3. This way, we will not make a distribution error. The problem now turns into:

2x + (-3x -3)/(x+1)(x)= 5

3) Solve: Doing some distribution and cross multiplication, we get
2x + -3x + -3 = 5x^2 + 5x
-x -3 = 5x^2 + 5x
= 5x^2 + 6x + 3