Q) Let f(x)=(2x/2x^2+5x+2) AND g(x)=(1/1+x).Find the set of real values of x for which f(x)> g(x) .

A) f(x) > g(x)
f(x) - g(x) > 0

2x/ (2x^2 + 5x+ 2) - 1 / (1+x) > 0

2x / (2x+1)(x+2) - 1/1+x > 0

-3x - 2 / (2x-1)(x+2)(x+1) > 0

3x+2 / (2x-1)(x+2)(x+1) <>

x not equal to -1, -2, -1/2 as we get 0 in denominator... and x not equal to -2/3 as numerator becomes 0

Now apply wave curve method.

x E (-2, -1) U (-2/3, -1/2)

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