Question

How do you simplify `(w-3)/(w^2-w-20)+w/(w+4)`?

Answer 1

`(w^2-4w-3)/((w-5)(w+4))`

Explanation:

Before we can add the fractions we require them to have a `color(blue)"common denominator"`

`"factorise the denominator of the left fraction"`

`rArr(w-3)/((w-5)(w+4))+w/(w+4)`

`"To obtain a common denominator"`

multiply the numerator/denominator of`w/(w+4)" by " (w-5)`

`rArr(w-3)/((w-5)(w+4))+(w(w-5))/((w-5)(w+4))`

Now we have a common denominator, add the numerators leaving the denominator as it is.

`rArr(w-3+w^2-5w)/((w-5)(w+4))`

`=(w^2-4w-3)/((w-5)(w+4))to(w!=5,w!=-4)`