Alg_Complete

# 2 z 1 2 z 4 z 1 2 z 4 z 2 1 z 2 2 z 5 2 z

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Unformatted text preview: x - 2 + 15 x 2 = 6 x5 [Return to Problems] (b) 2 z -1 z +1 z + 2 In this case there are only two factors and they both occur to the first power and so the least common denominator is. lcd : ( z + 1) ( z + 2 ) Now, in determining what to multiply each part by simply compare the current denominator to the least common denominator and multiply top and bottom by whatever is “missing”. In the first term we’re “missing” a z + 2 and so that’s what we multiply the numerator and denominator by. In the second term we’re “missing” a z + 1 and so that’s what we’ll multiply in that term. Here is the work for this problem. 2 ( z + 2) ( z - 1) ( z + 1) = 2 ( z + 2 ) - ( z - 1) ( z + 1) 2 z -1 = z + 1 z + 2 ( z + 1)( z + 2 ) ( z + 2 )( z + 1) ( z + 1)( z + 2 ) The final step is to do any multiplication in the numerator and simplify that up as much as possible. 2 z - 1 2 z + 4 - ( z - 1) 2 z + 4 - z 2 + 1 - z 2 + 2 z + 5 2 = = = z +1 z + 2 ( z + 1)( z + 2 ) ( z + 1)( z + 2 ) ( z + 1)( z + 2 ) Be careful with minus signs and parenthesis when doing the subtraction. [Return to Problems] (c) y 2 3 + y - 2 y +1 y -1 y + 2 2 Let’s first factor the denominators and determine...
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