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Solve By Wavy Curve Method?
x-1 <1
x2-4x+3
Dear Rohan
(x-1)/(x2-4x+3) - 1 < 0
(-x2+5x-4)/(x2-4x+3) < 0
multiply with -1 both the sides, sign will reverse
(x2-5x+4)/(x2-4x+3) > 0
(x-1)(x-4)/(x-1)(x-3) > 0
For real solution denominator ≠ 0 hence x≠1,3
x-1 will be cancelled
now it becomes
(x-4)/(x-3) > 0
plot the number line
+ 3 __ 4 +
hence solution is
(-∞,3) U (4,∞) - {1}
or you can also write it as
(-∞,1) U (1,3) U (4,∞)
All the best.
AKASH GOYAL
AskiitiansExpert-IITD
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