rational expression

Question

2/w+2 -3/w + w+10/w^2-4

 

Answer 1

2/(w+2)-3/w+(w+10)/(w²-4)

2/(w+2)-3/w+(w+10/(w-2)(w+2)

LCM is w(w-2)(w+2)

2(w)(w-2)-3(w-2)(w+2)+(w+10)w/w(w-2)(w+2)

2w²-4w-3w²+12+w²+10w/w(w-2)(w+2)

combine similar terms in the numerator

(6w+12)/w(w-2)(w+2)

factor the numerator

6(w+2)/w(w-2)(w+2)

simplify

6/w(w-2)

 

 

 

 

Answer 2

OK, Irene.  I believe your equation is:  2/(w+2) - 3/w + (w+10)/(w²-4).

 

If this is correct, the LCD (least common denominator) is w(w-2)(w+2).

 

The first term only has (w+2) and therefore, needs to be multiplied by w(w-2)/(w)(w-2).

 

The second term only has w, and therefore needs to be multiplied by (w-2)(w+2)/(w-2)(w+2).

 

The third term needs to be multiplied by w/w.

 

Putting this all together, we get:

 

((2)(w)(w-2)-3(w-2)(w+2)+(w+10)(w))/(w)(x+2)(w-2)).

 

After simplifying, I get:  (6w-12)/((w)(w+2)(w-2)).

 

Note there is a common factor in the numerator and denominator: 6(w-2)/((w)(w+2)(w-2))

 

So the final answer becomes:  6/((w)(w+2))

 

I hope this helps.