Question

4.73. Uprość wyrażenia:
c) |1/x-1| * |1-x|
d) 3|x-2|-|6+3x|
e) |3x+9/4| * |4/3+x|

Z góry dzięki :) daje naj c:

Answer 1

c)
|1/(x-1)|*|1-x| = ?
|1/(x-1)|*|1-x| = |1-x|/|x-1|
 x ≠ 1
 x > 1
|1-x|/|x-1| = (x-1)/(x-1) = 1
 x < 1
|1-x|/|x-1| = (1-x)/(1-x) = 1
d)
3|x-2|-|6+3x| = ?
x  -  2 < 0    x < 2
6 + 3x < 0   x <-2
 x < -2
3|x-2|-|6+3x| = 3(-x + 2) - (-6 - 3x) = -3x + 6 + 6 + 3x = 12
-2 < x < 2
3|x-2|-|6+3x| = 3(-x+2) - ( 6 + 3x) = -3x + 6 - 6 - 3x =-6x
x > 2
3|x-2|-|6+3x| = 3( x - 2) - ( 6 + 3x) =  3x - 6 - 6 - 3x =-12
e)
|(3x+9)/4| * |4/(3+x)| = ?
 x ≠ -3
x ∈ (- ∞;-3) ∪ (-3; +∞)
|(3x+9)/4|*|4/(3+x)| = 3|(x+3)| * |1/(3+x)| = 3|x+3|/|x+3| = 3