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# Solve By Wavy Curve Method?    x-1   <1 x2-4x+3

Grade:12th pass

## 1 Answers

AKASH GOYAL AskiitiansExpert-IITD
419 Points
10 years ago

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

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