Find the following sum:

(Problem in comments...)

Question

Find the following sum:

(Problem in comments...)

anonymous · Answer

$$\frac{ a-6 }{ a-5 }+\frac{ 7 }{ a^2-3a-10 }$$

anonymous · Answer

Is this -1 too? @ganeshie8 I used to website & that's what it said, but it automatically put =0 at the end.

kainui · Answer

So in order to add fractions you have to find a common factor so that you can add them up.

For instance, what's 1/2 + 1/4? Well you can't just add them up right away, you have to rewrite 1/2 as 2/4 so that you have 2/4+1/4 which is 3/4. You need to so something similar here.

The answer is not -1.

anonymous · Answer

I know I have to factor out a^2-3a-10, which is (a -5)(a+2), right?

kainui · Answer

Yep! So you need to multiply the left fraction by (a+2)/(a+2) so that you can add the fractions together.

anonymous · Answer

$$\frac{ a-6(a+2) }{ a-5(a+2) }$$
Do I leave the left side as is?
$$\frac{ 7 }{ (x-5)(x+2) }$$
Or add the (a+2) to the 7 as well?

anonymous · Answer

*right side

kainui · Answer

The right side stays as is since the denominators (bottom parts of the fraction) are the same, so we can now just add them up.

anonymous · Answer

Ok, kind of confused on how to add them, would it be 2a-4 & 2a-3?

kainui · Answer

So you'll multiply the polynomial on top and then add those parts together then you can factor it again.

anonymous · Answer

I'm lost lol

kainui · Answer

$$\frac{(6-a)(a+2)}{(a-5)(a+2)}+\frac{7}{(a-5)(a+2)}=\frac{(6-a)(a+2)+7}{(a-5)(a+2)}$$ That make sense or are you stuck somewhere else?

anonymous · Answer

ooooh, just put it all together, got it now.

kainui · Answer

Yeah, but it's not in its simplest possible form! You need to multiply the top part together then factor it out again.

anonymous · Answer

So, 6a-2a+7?

anonymous · Answer

or a^2 + 12+7?

kainui · Answer

I accidentally wrote the top part having (6-a) when it really should be (a-6) whoops

So it'll be:

(a-6)(a+2)+7=a^2-6a+2a-12+7=a^2-4a+5

Then factor it out again.

kainui · Answer

I must be tired, because that should be -5 not +5 since -12+7=-5!

anonymous · Answer

So, it'll be $$\frac{ a^2-4a-5 }{ (x-5)(x+2) }$$?

kainui · Answer

Yeah, now factor the top and you should be able to simplify it by dividing out one of the factors in common!

anonymous · Answer

$$\frac{ (a-5)(a+1) }{ (a-5)(a+2) }$$
They cancel out & you have:
$$\frac{ (a+1) }{ (a+2) }$$?