Simplifying Rational Expressions Monomials and Binomials
Simplifying rational expressions involves factoring, reducing coefficients, eliminating common factors, and determining restrictions. This process is demonstrated through various examples in the images provided.
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11.1 Simplifying Rational Expressions Monomials and Binomials
Simplifying Rational Expressions1.Factor 2.Reduce coefficients 3.Eliminate common factors 4.Determine restrictions Hi! I m Fred!
EX 1 Simplify 1. Factor 2. Reduce 3. Eliminate 4. Determine restrictions 2 21 7 a a 3 3 a a 0
EX 2 Simplify 2 18 4 d + 18 4 d + 9 2 d + 9 2 d + d 8 2 1. Factor 2. Reduce 3. Eliminate 4. Determine restrictions 2 d d ( ) 2 2 d ( ) 2 2 d 4
EX 3 26 2 x Simplify 1. Factor 2. Reduce 3. Eliminate 4. Determine restrictions + 3 91 7 + x x ( x 2 ) + 2 13 2 7 x x + x 2 2 7 13 1 none 13x
EX 4 2 6 2 3 2 Simplify 1. Factor 2. Reduce 3. Eliminate 4. Determine restrictions 3 9 3 n n n ( ) 3 n 1 3 32 n
EX 5 2 x Simplify 8 x ( 4 2 2 8 x ) 2 4 x ( )( ) + 2 x x 2 x 2,4 x+ 2
EX 6 2 x x 9 Simplify + 2 17 )( )( x 2 81 ( ) + + 2 x 1 9 9 x x x ( ) 9 2 x 1 x x 9,9 9
EX 7 2 x Simplify 64 + 2 72 x x + + (8 ( x )(8 8)( ( 1 8 x 8 x ) x x 9) ) x + x + 9 x x 9,8 + 9
11.2 Multiplying and Dividing Rational Expressions
Simplifying Rational Expressions 1. Multiply by the Reciprocal When you divide rational expressions, 2. Factor 3. Reduce coefficients 4. Eliminate common factors 5. Determine restrictions
EX 1 Simplify 1. Factor 2. Reduce 3. Eliminate 4. Determine restrictions 2 2 x x 4 x x 0 2
EX 2 Simplify 1. Factor 2. Reduce 3. Eliminate 4. Determine restrictions 2 4 5 + ( ( z 3 z z z ) 3 2 z ) 4 5 + z 4,0 5 z
EX 3 x x + Simplify 2 x + + + 2 4 8 12 1 6 8 2 x x x 2 1. Factor 2. Reduce 3. Eliminate 4. Determine restrictions ( )( ) ( ) + ( 2 x+ x 6 x+ 2 x x 4 ( x+ x+ 2 4 ) 2 ) 2 6 x 4,2 4
1. Multiply by the Reciprocal EX 4 Simplify 8 3x 2 x 2. Factor 3. Reduce 4. Eliminate 5. Determine restrictions 2 2 x 8 3 2 x 4 x x 0 3
1. Multiply by the Reciprocal EX 5 3 Simplify 8 3 3 8 x+ + + 6 4 x x 18 x+ 2. Factor 3. Reduce 4. Eliminate 5. Determine restrictions 3 6 4 18 ( ) x+ 18 3 2 3 ( 4 ) x+ 2 9 1 8 x = 2 72
1. Multiply by the Reciprocal EX 6 2 x x + 2 x x + Simplify 1 6 x + 6 1 1 x 2 6 2 x 2. Factor 3. Reduce 4. Eliminate 5. Determine restrictions 3,1,2 x + 2 x x 1 2 6 x ( ) ( ( )( )( 3 ) x+ x + + x+ 2 3 1 1 2 x x x x ( x ) ) 1 2 1 2
