Download Lesson 82: Algebraic Simplifications

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