Question

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Which of the following is the simplified form of x plus 7 over 2 x plus 12 plus the fraction 6 over x squared minus 36 ?

x plus 5 over 2 times the product x minus 6

x minus 5 over 2 times the product x plus 6

x minus 5 over 2 times the product x minus 6

x plus 5 over 2 times the product x plus 6

Answer 1

it makes it easier to read if you type out the equations how they look instead of writing out the words.. ahah

like:\[\frac{ x+7 }{ 2x +12}+\frac{ 6 }{ x^{2}-36 }\]


the way you write out the words makes it confusing since they could actually mean totally different things, i'm just assuming this is what you meant

Answer 2

so you want to factor the denominators first, then find a least common denominator so you can add the numerators together. then just simplify

Answer 3

Okay and yes that's what meant

Answer 4

@Luigi0210

Answer 5

What do you need? :P

Answer 6

Did you get common denominators?

Answer 7

No i'm confused... my friend tried explaining it differently now i'm all math out confused. D;

Answer 8

Can factor the bottoms?

Answer 9

\[\frac{ x+7 }{ 2(x+6) }+\frac{ 6 }{ (x-6)(x+6) }\]

Answer 10

okay I see, but do we cross out the bottom part or?

Answer 11

Nope, nothing cancels. get common denominators

Answer 12

so how do I do that, would it just be 6?

Answer 13

:l

Answer 14

no?

Answer 15

I'm sorry, D:

Answer 16

is it this
\[\frac{ x+7 }{ 2x +12}+\frac{ 6 }{ x^{2}-36 }\]?

Answer 17

yes..

Answer 18

oh i see @Luigi0210 got it, nvm

Answer 19

?

Answer 20

Sorry about that.. but yea, get common denominators.. make the bottom the same for both expressions.

Answer 21

so its not 6

Answer 22

factor as shown to get
\[\frac{ x+7 }{ 2(x+6) }+\frac{ 6 }{ (x-6)(x+6) }\] then the least common denominator will be
\[2(x+6)(x-6)\]

Answer 23

Unless my math skills are gone

Answer 24

so that will be 2x+12 x's 2x-12?

Answer 25

then you combine like terms?

Answer 26

\[\frac{ x+7 }{ 2(x+6) }+\frac{ 6 }{ (x-6)(x+6) }\]
\[\frac{ x+7 }{ 2(x+6) }\times \frac{x-6}{x-6}+\frac{ 6 }{ (x-6)(x+6) }\times \frac{2}{2}\]
\[\frac{(x+7)(x-6)}{2(x+6)(x-6)}+\frac{12}{2(x-6)(x+6)}\]
\[=\frac{(x+7)(x-6)+12}{2(x-6)(x+6)}\]

Answer 27

I'm lost, I'm sorry.

Answer 28

yeah this is a bit annoying, but it is how you add fractions

Answer 29

Okay..

Answer 30

suppose we replace \(x\) by 11

Answer 31

okay..

Answer 32

so \(x+6=11+6=17\) and \(x-6=11-6=5\) and also \((x+6)(x-6)=11\times 5=55\) and \(x+7=11+7=18\) and finally \(2(x+6)=2(11+6)=34\)
then how would you add

Answer 33

\[\frac{18}{34}+\frac{6}{55}\]

Answer 34

you have to find a least common denominator for these fractions

Answer 35

Okay,

Answer 36

DAMN

Answer 37

i made a mistake \(11+6=17\) and \(11-6=5\) so \((x+6)(x-6)=5\times 17=85\)
and you have to add
\[\frac{18}{34}+\frac{6}{85}\] that is what i meant

Answer 38

how do you do it? you have to find a least common multiple of \(34\) and \(85\)

Answer 39

uhm, whats happening satellite?

Answer 40

and to do that, you need to factor these numbers
\(34=2\times 17\) and \(85=5\times 17\) so the least common denominator will be
\[2\times 17\times 5\]

Answer 41

then to add you would do this
\[\frac{18}{34}\times \frac{5}{5}\] and
\[\frac{6}{85}\times \frac{2}{2}\] that would make the denominators the same, so you can add

Answer 42

\[\frac{18\times 5}{170}+\frac{6\times 2}{170}=\frac{18\times 5+6\times 2}{170}\]

Answer 43

it is exactly the same with variables. you find a least common multiple of the denominators, and then multiply each fraction top and bottom by what you need to put both fractions with the same denominator

Answer 44

for \(34\) and \(85\) you needed a 2, a 5 and a 17

for\(2(x+6)\) and \((x+6)(x-6)\) you need a \(2\) , a \(x+6\) and a \(x-6\)

Answer 45

that is my explanation of this line
\[\frac{ x+7 }{ 2(x+6) }\times \frac{x-6}{x-6}+\frac{ 6 }{ (x-6)(x+6) }\times \frac{2}{2}\] you are putting each fraction over the same denominator, so you can add

don't let the stupid \(x\) cloud the idea, it is just the same as with numbers

Answer 46

Sorrrrrrrrrrry, I left and forgot to say ill brb... D:

Answer 47

@satellite73