Solve the inequality \(\frac{\left( x+a \right)\left( x-b \right)}{x{{\left( x-c \right)}^{2}}}

Question

Solve the inequality $\frac{\left( x+a \right)\left( x-b \right)}{x{{\left( x-c \right)}^{2}}}<0$, where $a,b,c\in {{\mathbb{R}}^{+}}$ and $0 < c < b < a$. Hence, find the range of values of $x$ which satisfy $\frac{\left( \ln x+a \right)\left( \ln x-b \right)}{\left( \ln x \right){{\left( c-\ln x \right)}^{2}}}<0$.[5]

Accepted Answer

$x<-a$ or $0 < x < b$ and $x
e c$; $0 < x <{{e}^{-a}}$ or $1 < x <{{e}^{b}}$ and $x
e {{e}^{c}}$

2011 AJC P1 Q3

2011 AJC P1 Q3

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