SOLUTION: Help please? Simplify the sum. w^2 +2w-24/w^2+w-30 +8/w-5

Question 712162: Help please? Simplify the sum.

w^2 +2w-24/w^2+w-30 +8/w-5
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
If the expression is:

then please post it with parentheses around multiple-term numerators and denominators, like:
(w^2 +2w-24)/(w^2+w-30) +8/(w-5)
What you posted, without the parentheses, meant:

Clearly posted questions will get faster responses.

To add these (or any) fractions we must first make the denominators be the same. To make the denominators the same we first look for the lowest common denominator (LCD). To find the LCD we must see what the factors of the denominators are:

This makes the LCD:
(w+6)(w-5)

We could go ahead and make the second fraction's denominator equal to the LCD. But if we are a little clever and look at the first term's numerator we will notice that it factors, too:

Since the first fraction's numerator and denominator share a factor, w+6. So it will reduce. Reducing the first fraction will make things easier so that is where we will start:

Canceling the common factor:

leaving:

Not only did the first fraction reduce, but the denominators ended up being equal! So we can go directly to the addition:

which simplifies to:

This is the simplified sum.
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