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EAMCET Engineering 2010 Solved Paper

Section: Mathematics

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Question : 62 of 160

Marks: +1, -0

\{ x \in R : \;\frac{14x}{x+1} - \;\frac{9x-30}{x-4} < 0 \}

$(-1,4)$
$(1,4) \cup (5,7)$
$(1,7)$
$(-1,1) \cup (4,6)$

Solution:

\; \{ x \in R : \;\frac{14x}{x+1} - \;\frac{9x-30}{x-4} < 0 \}

\;\;\frac{14x(x-4)-(9x-30)(x+1)}{(x+1)(x-4)} < 0

\;\;\frac{14x^2-56x-(9x^2-30x+9x-30)}{(x+1)(x-4)} < 0

\;\;\frac{14x^2-56x-9x^2+30x-9x+30}{(x+1)(x-4)} < 0

\;\;\frac{5x^2-35x+30}{(x+1)(x-4)} < 0

\;\;\frac{x^2-7x+6}{(x+1)(x-4)} < 0, \;\frac{(x-1)(x-6)}{(x+1)(x-4)} < 0

Drawn number line,

Hence,

x \in (-1,1) \cup (4,6)

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