Question

Consider the following functions. f(x)=9/x​g(x)= 11/x+11.​
Find (f+g)(x)

Answer 1

(f + g )(x) =
`(20x+99)/(x(x+11))`

Explanation:

(f + g )(x)

= f(x) + g(x)

=
`(9)/(x)` +
`(11)/(x+11)`

before adding we require the fractions to have a common denominator

multiply numerator and denominator of first fraction by (x + 11)

multiply the numerator and denominator of second fraction by x

=
`(9(x+11))/(x(x+11))` +
`(11x)/(x(x+11))`

add the numerators over the common denominator

=m
`(9x+99+11x)/(x(x+11))`

=
`(20x+99)/(x(x+11))`