Question

HELP ? Simplify the sum. State any restrictions on the variables.
x-2/x+3 + 10x/x^2-9

Answer 1

\[\frac{ x-2 }{ x+3 }\div \frac{ 10x }{ x^2-9 }\]

Answer 2

What looks factorable?

Answer 3

ummmmm.... i dont really understand what you mean @dtan5457

Answer 4

To simplify rational expressions, you want to cross out as many terms as possible. Look at x^2-9.

What does that simplify to?

Answer 5

i dont know D: 1?

Answer 6

sorry math is my worst subject

Answer 7

\[a^2-b^2=(a+b)(a-b)\]

Answer 8

x^2-9=

(x+3)(x-3)

Answer 9

Got it?

Answer 10

yee

Answer 11

Ok, now if you remember from 5th grade lol, what do you do when you divide fractions?

Answer 12

multiply?

Answer 13

@chlobohoe please avoid giving direct answers :D

Answer 14

You switch the 2nd fraction (reciprocal), then multiply

Answer 15

ye

Answer 16

wait what fractions? ahahaha

Answer 17

\[\frac{ x-2 }{ x+3 } \times \frac{ (x+3)(x-3) }{ 10x }\]

Answer 18

Once you switch it, it should look like that. Now what terms can we cross out?

Answer 19

ohhh um ..x+3 and 10x?

Answer 20

dont you suppose to multiply going straight across right? or no?

Answer 21

You are, but if there is a same term in the numerator and denominator, you can cross them out.

Answer 22

In this case's x+3

Answer 23

\[\frac{ (x-2)(x-3) }{ 10 }\]

Answer 24

Opps forgot the x on the 10

Answer 25

yea i understand

Answer 26

so then do that fraction stay like that?

Answer 27

Kk wait a second. I think I'm gonna jump off a building

Answer 28

hahah what's wrong

Answer 29

Your question says to add..I divided.

Answer 30

ohhh .. i wouldnt have noticed loool ..

Answer 31

If you will excuse me for 2 minutes while I redo this problem that will be great

Answer 32

okiee that's fine

Answer 33

Ok got it. Let's do this again...sorry

Answer 34

\[\frac{ x-2 }{ x+3 }+\frac{ 10x }{ x^2-9 }\]
Factor out x^2-9

Answer 35

We said that was x+3(x-3)

Answer 36

yee

Answer 37

\[\frac{ x-2 }{ x+3 }+\frac{ 10x }{ (x-3)(x+3) }\]

Answer 38

When we add fractions, they must have the same denominator

Answer 39

Therefore, we multiply x-2/x+3 by x-3

Answer 40

\[\frac{ (x-3)(x-2) }{ (x+3)(x-3) }+\frac{ 10x }{ (x-3)(x+3) }=\frac{ x^2-6x+6+10x }{ }\]

Answer 41

The denominator would still be (x+3)(x-3)

Answer 42

\[\frac{ x^2+4x+6 }{ (x+3)(x-3) }\]

Answer 43

You can factor the top part as
\[\frac{ (x+3)(x+2) }{ (x+3)(x-3) }\]

Answer 44

Cross out the x+3 and you get\[\frac{ x+2 }{ x-3 }\]

Answer 45

ohhhhhhhhh so you cancel out the same thing that's on top i see ..

Answer 46

THANK YOUUUUUUUUUUUUUU for helping

Answer 47

Great explaining @dtan5457

Answer 48

Yeah, it's just too bad I did the whole problem wrong by dividing instead of adding at first

Answer 49

Do you know what the restrictions are?

@rawmoli

Answer 50

no?

Answer 51

Whenever you have rational fractions, usually the only restriction is that the denominator CANNOT be 0.

Answer 52

\[\frac{ x-2 }{ x+3 }\]

Answer 53

What x value would make this invalid?

Answer 54

2?

Answer 55

sorry i dont understand aahah ..

Answer 56

Denominator can't be 0, not numerator

Answer 57

ohhhhh

Answer 58

So x can't be..?

Answer 59

no

Answer 60

i think

Answer 61

lol take your time

Answer 62

x+3=0

x=?

Answer 63

-3?

Answer 64

@dtan5457

Answer 65

x=-3,

but that's just one of the restrictions

Answer 66

\[\frac{ x-2 }{ x+3 }+\frac{ 10x }{ x^2-9 }\]

Answer 67

actually i'm not 100% sure but i'm pretty sure if x=3, that would make the 2nd fraction have a 0 and be restricted

Answer 68

@Nnesha

Answer 69

OH SO I WAS RIGHT WITH -3? yesssssssssssssssssssss

Answer 70

Yeah, but there might be one more, but i'm not 100% sure so..

Answer 71

ohh okiee

Answer 72

thank you for everything