Question

C) 3x²/x+2 = 2-x

d)5x+3/4x-3=4x-3/5x+3

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Answer 1

C) 3x²/x+2 = 2 - x

        3x²        2 - x
       ------ = ---------
       x + 2        1
3x² = (x+2) (2-x)
3x² = x (2-x) + 2 (2-x)
3x² = 2x - x² + 4 - 2x
3x² - 2x + x² - 4 + 2x = 0
4x² - 4 = 0 
4x² = 4
x² = 4:4
x² = 1
x' = 1
x'' = -1

S = {-1,1}

B) 5x + 3       4x - 3
     --------  =  ----------
     4x - 3       5x + 3

(4x -3) (4x -3) = (5x +3) (5x + 3)
4x (4x -3) -3 (4x-3) = 5x (5x+3) +3 (5x + 3)
16x² - 12x -12x + 9 = 25x² + 15x + 15x + 9
16x² - 25x² - 24x - 30x + 9 - 9 = 0
-9x² - 54x = 0
x (-9x - 54) = 0
x' = 0

-9x -54 = 0
-9x = 54
x'' = 54 : -9
x'' = -6

S = {0,-6}