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Tuesday 9th of August
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 Depdendent Variable

 Number of equations to solve: 23456789
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 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

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# Multiplying and Dividing Rational Expressions

## Ι Multiplying Rational Expressions

To MULTIPLY rational expressions, factor all polynomials and reduce first, then multiply numerators by numerators and denominators by denominators. [Always check the result to see if it will reduce to simpler form.]

Caution: You can cancel only complete factors. You cannot cancel a piece of a sum. You cannot cancel the 5 in the fraction nor the â€œxâ€ in the expression

NOTE: Look at all of the polynomials in the rational expressions and start factoring the ones you recognize first. You can use these to help factor the others using the â€œtrial and errorâ€ method. If all else fails you always use the GN (grouping number) method to factor. Reduce the factored expressions and collect factors.

If binomial differences have the letters in opposite order, factor out (-1).

Examples

1)

2)

## ΙΙ Dividing Rational Expressions

To DIVIDE by a rational expression, CHANGE TO MULTIPLY by the INVERSE, or (reciprocal).

Examples

1) Change to MULTIPLY:

Factor Reduce

2) Change to MULTIPLY:

Factor:

Reduce: