PLEASE HELP ME!!!!!!! I AM NOT GOOD AT MATH!Given the function f(x)= \frac{x^2+7x+10}{x^2+9x+20} Describe where the function has a hole and how you found your answer.

Only hole of function [tex]f(x) = \frac{x^{2}+7x+10 }{x^{2}+9x+20 }[/tex] is at x=(-4)Step-by-step explanation:Given the function is [tex]f(x) = \frac{x^{2}+7x+10 }{x^{2}+9x+20 }[/tex]In order to find holes of any function, you should find when function is becoming undefined or say " infinity" Given function is polynomial function.It will become undefined become denominator become zero[tex]x^{2}+9x+20=0[/tex]Solving for x value when denominator become zero[tex]x^{2}+9x+20=0\\x^{2}+5x+4x+20=0\\x(x+5)+4(x+5)=0\\(x+4)(x+5)=0[/tex]we get possible holes at x=(-4) and x=(-5)Check whether you can eliminate any holesNow, Solving for x value when numerator become zero[tex]x^{2}+7x+10=0\\x^{2}+5x+2x+10=0\\(x+5)(x+2)=0[/tex]x=(-5) and x=(-2)x=(-5) is common is both numerator and denominator.So that, we can eliminate it.[tex]f(x) = \frac{(x+5)(x+2)}{(x+5)(x+4)}[/tex][tex]f(x) = \frac{(x+2)}{(x+4)}[/tex]Therefore, Only hole of function [tex]f(x) = \frac{x^{2}+7x+10 }{x^{2}+9x+20 }[/tex] is at x=(-4)