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20 March, 19:42

Show that each algebraic fraction simplifies to the given expression.

a) 2/x+1 + 5/x+2 = 3 simplifies to 3x² + 2x - 3 = 0

b) 3/4x+1 - 4/x+2 = 2 simplifies to 8x² + 31x + 2 = 0

c) 2/2x-1 - 6/x+1 = 11 simplifies to 22x² + 21x - 19 = 0

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Answers (2)
  1. 20 March, 20:03
    0
    Hello,

    a)

    we suppose that x≠-1 and x≠-2

    2 / (x+1) + 5 / (x+2) = 3

    ==>2 (x+2) + 5 (x+1) = 3 (x+1) (x+2)

    ==>7x+9=3x²+9x+6

    ==>3x²+2x+3=0

    b)

    we suppose that x≠-1/4 and x≠-2

    3 / (4x+1) - 4 / (x+2) = 2

    ==>3 (x+2) - 4 (4x+1) = 2 (4x+1) (x+2)

    ==>-13x+2=8x²+18x+4

    ==>8x²+31x+2=0

    c)

    we suppose that x≠1/2 and x≠-1

    2 / (2x-1) - 6 / (x+1) = 11

    ==>2 (x+1) - 6 (2x-1) = 11 (2x-1) (x+1)

    ==>-10x+8=22x²+11x-11

    ==>22x²+21x-19=0
  2. 20 March, 20:10
    0
    a) 2/x+1 + 5/x+2 = 3 simplifies to 3x² + 2x - 3 = 0

    2 (x+2) + 5 (x+1) = 3 (x+2) (x+1)

    2x + 4 + 5x + 5 = (3x+6) (x+1)

    7x + 9 = 3x² + 3x + 6x + 6

    7x + 9 = 3x² + 9x + 6

    0 = 3x² + 9x - 7x + 6 - 9

    0 = 3x² + 2x - 3

    b) 3/4x+1 - 4/x+2 = 2 simplifies to 8x² + 31x + 2 = 0

    3 (x+2) - 4 (4x+1) = 2 (x+2) (4x+1)

    3x + 6 - 16x - 4 = (2x+4) (4x+1)

    -13x + 2 = 8x² + 2x + 16x + 4

    0 = 8x² + 18x + 13x + 4 - 2

    0 = 8x² + 31x + 2

    c) 2/2x-1 - 6/x+1 = 11 simplifies to 22x² + 21x - 19 = 0

    2 (x+1) - 6 (2x-1) = 11 (x+1) (2x-1)

    2x + 2 - 12x + 6 = (11x+11) (2x-1)

    -10x + 8 = 22x² - 11x + 22x - 11

    0 = 22x² + 11x + 10x - 11 - 8

    0 = 22x² + 21x - 19
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