Solve the inequality.

x + 1 / (x-1)^2 > 1


The answer is (-∞,0) U (3,∞)

Asked by prakhar.dpm | 8th Sep, 2019, 05:14: PM

Expert Answer:

fraction numerator x plus 1 over denominator left parenthesis x minus 1 right parenthesis squared end fraction greater than 1
rightwards double arrow x plus 1 greater than left parenthesis x minus 1 right parenthesis squared
rightwards double arrow x plus 1 greater than x squared minus 2 x plus 1
rightwards double arrow x squared minus 3 x less than 0
rightwards double arrow x left parenthesis x minus 3 right parenthesis less than 0
T h e r e space a r e space t w o space c a s e s colon space
C a s e space 1 colon
x less than 0 space a n d space x minus 3 greater than 0
rightwards double arrow x less than 0 space a n d space x greater than 3
T h e r e space i s space n o space c o m m o n space p o i n t space f o r space t h e space a b o v e space t w o space i n e q u a l i t y
S o comma space i t space i s space e m p t y
C a s e space 2 colon
x greater than 0 space a n d space x minus 3 less than 0
rightwards double arrow x greater than 0 space a n d space x less than 3
rightwards double arrow 0 less than x less than 3
rightwards double arrow x element of left parenthesis 0 comma 3 right parenthesis
H e n c e comma space t h e space a n s w e r space i s space left parenthesis 0 comma space 3 right parenthesis
T h e space a n s w e r space w i l l space b e space left parenthesis negative infinity comma 0 right parenthesis space union space left parenthesis 3 comma infinity right parenthesis space i f space t h e space i n e q u a l i t y space w o u l d space b e space fraction numerator x plus 1 over denominator left parenthesis x minus 1 right parenthesis squared end fraction less than 1

Answered by Renu Varma | 9th Sep, 2019, 10:43: AM

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