Question

Solve:
x-1
——— < 0
x²-4

Answer 1

Answer: x≠±2, x<±2, x>1, x<1, and x>±2

explanation:

for this equation to be true

Case 1

either (x-1) should be a negative while (x²-4) should be positive

which gives:-

x-1<0

so, x<1

also, x²-4>0

so, x²>4

⇒x>±2

Case 2:-

x-1>0 and x²-4<0

which gives

x>1 and x²-4<0

so, x>1 or x<±2

Case 3:-

either way, the denominator can't be 0

so, x²-4≠0

which gives,

x≠±2

compiling all, we have,

x≠±2, x<±2, x>1, x<1, and x>±2

These solutions can be pointed to as points on a number line and the behavior shows their discontinuity.

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