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Find the set of all x foir which (2x)/((...

Find the set of all `x` foir which `(2x)/((2x^2+5x+2))>1/((x+1))dot`

Text Solution

Verified by Experts

The correct Answer is:
`x in(-2,-1)uu(-(2)/(3),-(1)/(2))`
Given, `(2x)/(2x^(2)+5x+2)gt(1)/(x+1)`
`implies (2x)/((2x+1)(x+2))-(1)/((x+1))gt0`
`implies(2x(x+1)-(2x+1)(x+2))/((2x+a)(x+2)(x+1))gt0`
`implies(-(3x+2))/((2x+1)(x+1)(x+2))gt0,` using number line rule

`thereforex in(-2,-1)uu(-(2)/(3),-(1)/(2))`
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