Question

Questionf(2)Find R(2) where f(2)g(2)x² – a- 2 - 3010x + 100and g(2)-22 – 5x + 6611x + 110(Simplify your answer.)Provide your answer below:

Answer 1

Given that,

To find,

`R(x)=(f(x))/(g(x))`

where,

`f(x)=(x^2-x-30)/(10x+100)`
`g(x)=(-x^2-5x+66)/(11x+110)`

Simplifing f(x) and g(x), we get

`f(x)=(x^2-x-30)/(10x+10))=(x^2-6x+5x-30)/(10(x+10))`
`=(x(x-6)+5(x-6))/(10(x+10))=((x-6)(x+5))/(10(x+10))`
`f(x)=((x-6)(x+5))/(10(x+10))-----(1)`

This is the simplified form of f(x).

For g(x) we get,

`g(x)=(-x^2-5x+66)/(11x+110)=(x^2+5x-66)/(-11(x+10))`
`=(x^2+11x-6x-66)/(-11(x+10))=(x(x+11)-6(x+11))/(-11(x+10))`
`g(x)=((x+11)(x-6))/(-11(x+10))------(2)`

`(i)/(g(x))=(-11(x+10))/((x+11)(x-6))`

Now To find R(x), we get

`R(x)=(f(x))/(g(x))=f(x)*(1)/(g(x))`
`=((x-6)(x+5))/(10(x+10))*(-11(x+10))/((x+11)(x-6))`
`=(-11(x+5))/(10(x+11))`

we get,

`R(x)=(-11(x+5))/(10(x+11))`

Answer is:

`R(x)=(-11(x+5))/(10(x+11))`