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Simplify completely:

0 votes

Simplify completely:

asked Oct 2, 2018 in ALGEBRA 2 by anonymous
reshown Oct 2, 2018 by bradely

1 Answer

0 votes

1)

[ 5 + (x + 3)/(x - 1) ] / [ (3x - 1)/(1 - x^2) ]   =   [ 5 + (x + 3)/(x - 1) ] / [ (3x - 1)/(1 - x^2) ]

                                                                  =   [ (5(x - 1) + (x + 3)) / (x - 1) ] / [ (3x - 1)/(1 - x)(1 + x) ]

                                                                  =   [ 5x - 5 + x + 3 / (x - 1) ] X [ (1 - x)(1 + x) / (3x - 1) ]

                                                                  =  [ 6x - 2 / (x - 1) ] X [ (1 - x)(1 + x) / (3x - 1) ]

                                                                  =  [ 2(3x - 1) / (x - 1) ] X [ (1 - x)(1 + x) / (3x - 1) ]

                                                                  =  [ 2(3x - 1)(1 - x)(1 + x) ] /  [ (x - 1)(3x - 1) ]

                                                                  =  [ 2(1 - x)(1 + x) ] /  [ (x - 1)]

                                                                  =  [ 2(1 - x)(1 + x) ] /  [ -1(1 - x)]

                                                                  =  [ 2(1 + x) ] /  [ -1]

                                                                  =  2(-1)(1 + x)

                                                                  =  - 2 (1 + x)

 

2)

[ 4 - 1/(x^2)] / [ 1/x - 2 ]   =  [ (4x^2 - 1)/(x^2)] / [ (1 - 2x)/x ]

                                       =  [ (4x^2 - 1)/x] / [ (1 - 2x) ]

                                       =  [ (2x - 1)(2x + 1) ] / [ x(1 - 2x) ]

                                       =  [ (2x - 1)(2x + 1) ] / [ x(-1)(2x - 1) ]

                                       =  [ (2x - 1) ] / [ - x ]

                                       =  - (2x + 1) /  x

Answer :

1)   [ 5 + (x + 3)/(x - 1) ] / [ (3x - 1)/(1 - x^2) ]   =   -2(x + 1)

2)   [ 4 - 1/(x^2)] / [ 1/x - 2 ]   =   - (2x + 1) /  x

answered Nov 7, 2018 by homeworkhelp Mentor

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