Which graph shows the solution set of ?

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 305 People

Which graph shows the solution set of x^2+9+20/x^2-x-20 > 0

Answered by maham237 @ 25/12/2020

Before we do anything, we can factorize the numerator and denominator:

$\dfrac{x^2+9x+20}{x^2-x-20}=\dfrac{(x+5)(x+4)}{(x-5)(x+4)}=\dfrac{x+5}{x-5}$

(the cancellation is valid as long as $x\neq-4$ ; $x=-4$ is not even in the domain of the right hand side, so we're good here)

Then

$\drac{x+5}{x-5}=\dfrac{x-5+10}{x-5}=1-\dfrac{10}{x-5}>0\implies1>\dfrac{10}{x-5}$

$\implies1015$

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