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Rational Expressions

In Math, “Rational Numbers” are just numbers that can be written as

and so on…..

Rational Expression are just polynomials that are written in the form
of a fraction.

If a rational expression has ONLY multiplication and division
involved, reducing it to simplest form is just a matter of cancelling
out common factors.

When a rational expression has addition or subtraction involved,
it must be REWRITTEN into an expression with ONLY
MULTIPLICATION & DIVION in order to be reduced to
simplest form. You CANNOT CANCEL OUT common terms
if they are not FACTORS (something being multiplied).

If we factor the polynomials in the numerator & denominator,
then we can cancel out COMMON FACTORS.

After factoring the denominator, we should notice that this rational expression would be
denominator) if x = 4 or if x= -2.
So we must state the restrictions that x ? 4 and x? -2

Now this “rational expression” is in the form of factors multiplied
together. You can now cancel the common factors.


How do we factor an expression when the coefficient of x2 is negative?
It’s easier to do if you factor out a -1 from the expression.

Example 1C


Multiplying Rational Expressions

This works the same as multiplying fractions, but make sure
to only cancel out FACTORS from top to bottom, not side
to side. Of course each expression must be FACTORED
before you can cancel out FACTORS.

Dividing Rational Expressions

The way to divide rational expressions is the same method as
dividing fractions. Just take the reciprocal of the divisor (the
rational expression after the division sign, รท ) and multiply.

First, factor the polynomials wherever possible.

Notice the (y-3x) and the (3x - y). We’ve seen this before.
Just change one expression to look like the other and multiply by -1.