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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Simplifying Rational Expressions

1. need to identify any restrictions on the value of the variables

a. IE what will make the denominator zero

i. 2xy = 0 .: x = 0, y = 0. .: x,y cannot equal zero are the restrictions

2. Now reduce the expression into simplest terms.

a. Look at factoring the numerator or the denominator first, then use exponent laws or cancelling like terms.

i. The value of x can be reduced

Factoring the numerator and/or denominator

1. Restrictions , x cannot equal +/- 3.

a. Via inspection or factoring (x-3)(x+3)

2. the expression reduces to 5(x -3)/(x-3)(x+3), which simplifies to 5/(x+3)

3. Note when graphing the function there is no change to the output of the function. The graph is the same using the un-simplified form or the reduced form. The reduced form is easier to work with while doing the graphing by hand

## Complex Factoring of a rational expression

1. Restrictions on the denominator m cannot equal 0, -1/2, 4/3.

a. Factor the denominator m(6m 2 -5m-4) m(m+.5)(m-1.33)

2. Nothing can be factored further as there is nothing in common on top and bottom

1. Factor the numerator and denominator (if possible)

a. Simply

b. Complex

c. Multiple factoring

2. State restrictions of the denominator a. the restrictions are any value that will make the denominator equal zero

3. Cancel any terms which are multiplied on top and bottom.

4. Write out the final terms and state any restrictions.