Prentice Hall Algebra 1

Chapter 11 Rational Expressions and Functions > 11-1 Simplifying Rational Expressions

Problem 2 Simplifying a Rational Expression Containing a Trinomial

What is the simplified form of 3 x − 6 x 2 + x − 6 ? fraction 3 x minus 6 , over x squared , plus x minus 6 end fraction . question mark State any excluded values.

Think	Write
To see if there are any common factors, factor the numerator and the denominator.	3 x − 6 x 2 + x − 6 = 3 ( x − 2 ) ( x + 3 ) ( x − 2 ) fraction 3 x minus 6 , over x squared , plus x minus 6 end fraction . equals . fraction 3 open x minus 2 close , over open x plus 3 close open x minus 2 close end fraction
Divide out the common factor x minus 2 . Simplify.	= 3 ( x − 2 ) 1 ( x + 3 ) 1 ( x − 2 ) = 3 ( x + 3 ) table with 2 rows and 1 column , row1 column 1 , equals . fraction 3 . open , cross out enclosing , x minus 2 , end crossout , close to the first , over open x plus 3 close sub 1 . open , cross out enclosing , x minus 2 , end crossout , close end fraction , row2 column 1 , equals . fraction 3 , over open x plus 3 close end fraction , end table
State the simplified form with any restrictions on the variable.	The denominator of the original expression is 0 when x equals negative 3 or x equals 2 . So the simplified form is 3 x + 3 , fraction 3 , over x plus 3 end fraction . comma where x not equal to negative 3 and x not equal to 2 .

✓ Got It?

What is the simplified form of the expression? State any excluded values.
1. 2 x − 8 x 2 − 2 x − 8 fraction 2 x minus 8 , over x squared , minus 2 x minus 8 end fraction
2. a 2 − 3 a + 2 3 a − 2 fraction eh squared , minus 3 eh plus 2 , over 3 eh minus 2 end fraction
3. 6 z + 12 2 z 2 + 7 z + 6 fraction 6 z plus 12 , over 2 , z squared , plus 7 z plus 6 end fraction
4. c 2 − c − 6 c 2 + 5 c + 6 fraction c squared , minus c minus 6 , over c squared , plus 5 c plus 6 end fraction

The numerator and denominator of x − 3 3 − x fraction x minus 3 , over 3 minus x end fraction are opposites. To simplify the expression, you can factor negative 1 from 3 minus x to get negative 1 open negative 3 plus x close comma which you can rewrite as negative 1 open x minus 3 close . Then simplify x − 3 − 1 ( x − 3 ) . fraction x minus 3 , over negative 1 open x minus 3 close end fraction . .

Problem 3 Recognizing Opposite Factors

What is the simplified form of 4 − x 2 7 x − 14 ? fraction 4 minus , x squared , over 7 x minus 14 end fraction . question mark State any excluded values.

Simplify (4 minus x squared) over (7x minus 14).
Image Long Description

Plan

When should you factor negative 1 from an expression?

You should factor negative 1 from eh minus x when factoring negative 1 results in a common factor.

The denominator of the original expression is 0 when x equals 2 . The simplified form is − x + 2 7 , negative . fraction x plus 2 , over 7 end fraction . comma where x not equal to 2 .

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Problem 2 Simplifying a Rational Expression Containing a Trinomial

Think

✓ Got It?

Problem 3 Recognizing Opposite Factors

Plan

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