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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