Respuesta :
Answer:
Given that,
To find,
[tex]R(x)=\frac{f(x)}{g(x)}[/tex]where,
[tex]f(x)=\frac{x^2-x-30}{10x+100}[/tex][tex]g(x)=\frac{-x^2-5x+66}{11x+110}[/tex]Simplifing f(x) and g(x), we get
[tex]f(x)=\frac{x^2-x-30}{10x+10)}=\frac{x^2-6x+5x-30}{10(x+10)}[/tex][tex]=\frac{x(x-6)+5(x-6)}{10(x+10)}=\frac{(x-6)(x+5)}{10(x+10)}[/tex][tex]f(x)=\frac{(x-6)(x+5)}{10(x+10)}-----(1)[/tex]This is the simplified form of f(x).
For g(x) we get,
[tex]g(x)=\frac{-x^2-5x+66}{11x+110}=\frac{x^2+5x-66}{-11(x+10)}[/tex][tex]=\frac{x^2+11x-6x-66}{-11(x+10)}=\frac{x(x+11)-6(x+11)}{-11(x+10)}[/tex][tex]g(x)=\frac{(x+11)(x-6)}{-11(x+10)}------(2)[/tex][tex]\frac{i}{g(x)}=\frac{-11(x+10)}{(x+11)(x-6)}[/tex]Now To find R(x), we get
[tex]R(x)=\frac{f(x)}{g(x)}=f(x)\times\frac{1}{g(x)}[/tex][tex]=\frac{(x-6)(x+5)}{10(x+10)}\times\frac{-11(x+10)}{(x+11)(x-6)}[/tex][tex]=\frac{-11(x+5)}{10(x+11)}[/tex]we get,
[tex]R(x)=\frac{-11(x+5)}{10(x+11)}[/tex]Answer is:
[tex]R(x)=\frac{-11(x+5)}{10(x+11)}[/tex]