Question

Can someone attempt to explain this:

x/(x+3)+(x+2)/(x+5)

Answer 1

Since the denominators are different, you need to first find a common denominator

Answer 2

Ok-

Answer 3

Here the least common denominator is just (x+3)(x+5)

Answer 4

wouldn't i need to multiply that to the top?

Answer 5

you would need to multiply something on the top to get the denominator to (x+3)(x+5), yes

Answer 6

ultimate confusion

Answer 7

so you know that a/b + c/d is not equal to (a+c)/(b+d) right?

Answer 8

mhm

Answer 9

It's equal to (ad + bc)/(bd)

Answer 10

because if you want the common denominator as bd, then a/b becomes ad/bd, and c/d becomes bc/bd
Now both denominators are equal, so you can add
ad/bd + bc/bd = (ad+bc)/bd

Answer 11

so x/(x+3) + (x+2)/(x+5) = (x(x+5) + (x+2)(x+3)/((x+3)(x+5))

Answer 12

I somewhat understand...but im still confused-

Answer 13

so the x(x+5) is by itself?

Answer 14

Sorry I don't know latex
It's
x(x+5) + (x+2)(x+3)

Answer 15

ohhhh ok that looks and makes more sense

Answer 16

makeshift fraction sign did wonders

Answer 17

lol

Answer 18

so I can cross out the (x+5) and (x+3) from the top and bottom right?

Answer 19

You don't cross out, you divide the top and bottom by the same number.
but you can't do that here because the x(x+5) term doesn't have an (x+3) and the (x+2)(x+3) term doesn't have an (x+5) term

Answer 20

yeah I've hit rock bottom

Answer 21

lol

Answer 22

i'm going to try to figure out how to do this based on what you said and if I do I will let you know, gracias <3

Answer 23

I don't think you can simplify any farther though, but sure

Answer 24

well yeah I still have to figure out how you got there xD

Answer 25

Sure lmao