Is (x + 1)/(x - 3) < 0 ?

(1) -1 < x < 1

(2) x^2 - 4 < 0

Can i use componendo dividendo here ?? (just checking as Im not sure)

(x + 1 + x -3 )/ (x + 1 - x + 3) < 0 (using a/b ===> (a + b)/(a - b)

(2x - 2)/(4) < 0

x/2 - 1/2 < 0

x/2 < 1/2 (adding 1/2 on both sides)

x < 1 (multiplying by 2 on both sides)

now take a look at the answer choices

1) -1 < x < 1 =====> clearly within our given value of x < 1 -----> hence ok

2) x^2 - 4 < 0

===> x^2 < 4

x < 2 or x > -2

so -2 > x > 2, if x is less than 1 than ok but if 1 < x < 2 then not ok

Hence ans is A)

Please help me out here? Need to verify this method before I applying it elsewhere

If its wrong, why is it wrong? Is it because we cannot apply componendo - dividendo to inequalities ?

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