A fraction consists of
("numerator")/("denominator") -> ("count")/("size indicator of what you are counting")numeratordenominator→countsize indicator of what you are counting
color(blue)("Important fact 1")Important fact 1
You can not DIRECTLY add or subtract the counts unless the size indicators are the same
color(blue)("Important fact 2")Important fact 2
Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way numbers look but not change their actual value.
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color(blue)([1/2color(red)(xx1)]+[2/(x+2)color(red)(xx1)][12×1]+[2x+2×1]
Is the same as:
color(blue)([1/2color(red)(xx(x+2)/(x+2))]+[2/(x+2)color(red)(xx2/2)] [12×x+2x+2]+[2x+2×22]
(x+2)/(2(x+2))+4/(2(x+2))x+22(x+2)+42(x+2)
(x+2+4)/(2(x+2)) " "=" "(x+6)/(2x+4)x+2+42(x+2) = x+62x+4
