  # Solving Equations with Rational Expressions

How to Multiply

• If two radicals are defined and have the
same index then we can multiply them . Example

• Multiply the following, check using the
table. Note

• It is important that the domain from the
original expression carry over to the
simplified version. So, the functions and do not represent the same function
since they have different domains and
ranges.

Simplifying and the Product
Rule

• Examples More Examples • Recall how to collect like terms. The • If two radicals are defined and have the
same index then we can divide them. Examples Differing Index

• If the two radicals to be multiplied or
divided have differing index, then we
need to fix that prior to doing the
arithmetic
. Example: More Examples How to Multiply (again)

• If there is more than one term in the
expression
then we need to treat
multiplication as if we were multiplying
polynomials. That is we need to use the
distributive property.
Examples Rationalizing the Denominator

• Many times we want clear a radical
from the denominator of an expression .
We do this by multiplying the
expression by 1.
Example Principal of Powers

If a=b then for any  exponent n
This is an "if- then" statement and the reverse
may not be true .That is :
If then a=b is not always true!

In each of the following equations, the first has been squared
To create the second. Solve each graphically to see what
effect squaring both sides of an equation has on the outcome. Caution!

• Raising both sides of an equation to an
even power may not produce an
equivalent equation . It is essential to
check your solutions. That is why the
NAG.
• Also, keep in mind that • Every equation will be investigated by
three methods: NAG!
Numerical
Algebraic
• Graphical
Solve the following NAG Problems Involving Functions

If ,find a such that f(a)=5 The Number i

• We define the number i such that and For Example Complex Numbers

• A complex number is any number that
can be written a + bi, where a and b are
real numbers .
The Set of Real Numbers

Real Numbers

Real Numbers Integers Whole Numbers Natural Numbers Irrational Numbers Set of Complex Numbers
Complex Numbers Real Numbers Integers Whole Numbers Natural Numbers Irrational Numbers Examples of Arithmetic  Applications of

The Pythagorean Theorem Special Right Triangles Distance Formula Equation of a Circle Prev Next

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