Simplify: (1)/((x+3)(x+4)) +(2)/((x+4)(x+5))

Question

Simplify:
`(1)/((x+3)(x+4)) +(2)/((x+4)(x+5))`

Answer 1

`(3x+11)/((x+3)(x+4)(x+5))`

Explanation:

Before adding we require the fractions to have a common denominator.

Multiplying the numerator/ denominator of the first fraction by (x + 5)

Multiplying the numerator/ denominator of the second fraction by (x + 3)

=
`(x+5)/((x+3)(x+4)(x+5))` +
`(2(x+3))/((x+3)(x+4)(x+5))`

Now add the numerators leaving the common denominator

=
`(x+5+2x+6)/((x+3)(x+4)(x+5))`

=
`(3x+11)/((x+3)(x+4)(x+5))`