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Lesson 82: Algebraic Simplifications There are three rules of algebra that stand above all the rest. Two of the rules cannot be used unless an equals sign is present, for these rules apply only to equations. 1. The same quantity can be added to both sides of an equation without changing the answer(s) to the equation. Give me an example. 2. Every term on both sides of an equation can be multiplied by the same quantity (except zero) without changing the answer(s) to the equation. Give me an example. The third rule can be used on the individual terms of an equation and can also be used on expressions that are not terms of an equation. With few exceptions, if no equals sign is present, this rule is the only rule that can be used. 3. The denominator and the numerator of an algebraic expression can be multiplied by the same quantity (except zero) without changing the value of the expression. We call this rule the denominator-numerator rule. In this lesson we will discuss the repeated use of the denominatornumerator rule to simplify expressions that are just a little more complicated. Example Simplify a 1+ a 1+ 1 x Answer: a(x + 1) x + 1 + xa Example: Simplify b a+ c x+ 1 y Answer: b(xy + 1) axy + a + cy HW: Lesson 82 #1-30