Question

How do you simplify `3/(w + 4) + 8/(3w) + 12/(w(w +4))`?

Answer 1

`3/(w+4)+8/(3w)+12/(w(w+4))=17/(3w)`

Explanation:

In `3/(w+4)+8/(3w)+12/(w(w+4))`, we have denominators as

`w+4`, `3w` and `w(w+4)`, whose LCD is `3w(w+4)`

so convertig all to common denomiator, we get

`3/(w+4)=3/(w+4)xx(3w)/(3w)=(9w)/(3w(w+4)`

`8/(3w)=8/(3w)xx(w+4)/(w+4)=(8w+32)/(3w(w+4)` and

`12/(w(w+4))=12/(w(w+4))xx3/3=36/(3w(w+4)`

Hence, `3/(w+4)+8/(3w)+12/(w(w+4))`

= `(9w+8w+32+36)/(3w(w+4)`

= `(17w+68)/(3w(w+4)`

= `(17(w+4))/(3w(w+4))`

= `(17cancel((w+4)))/(3wcancel((w+4)))`

= `17/(3w)`