Question

Simplify as completely as possible:
10/x+1 / 1/2 + 3/x+1

Answer 1

\[\frac{ \frac{ 10 }{ x+1 } }{ 1/2 + \frac{ 3 }{ x+1} }\]

Answer 2

what is the inner LCD in this case

Answer 3

Um.. x+1? o.o Dunno

Answer 4

close, it's actually 2(x+1)

Answer 5

now multiply every term by this inner LCD

Answer 6

to clear out the inner fractions

Answer 7

Okay one sec

Answer 8

ok

Answer 9

\frac{ \frac{ 20(10x+10 }{ 2x(x ^{2} +1)} } }{ \frac{ 6(3x+3) }{ 2x(x ^{2} +1 } }

Answer 10

Oh shoot that didn't show up .

Answer 11

20(10x+10)/2x(x^2+1)/1(1/2x+1/2) + 6(3x+3)/2x(x^2+1)

Answer 12

\[\large \frac{ \frac{ 20(10x+10 }{ 2x(x ^{2} +1)} } }{ \frac{ 6(3x+3) }{ 2x(x ^{2} +1 } }\]

right?

Answer 13

Yeah

Answer 14

Did you forget to multiply that by the 1/2 ?

Answer 15

ok the point of multiplying every term with 2(x+1) is to cancel out all the inner denominators

Answer 16

so 10/(x+1) times 2(x+1) leaves you with 10*2 = 20 since the x+1 terms cancel

Answer 17

see how I'm getting that bit?

Answer 18

So under the 20(10x+10) etc.. would be / 20 + 6(etc.) ?

Answer 19

You there @jim_thompson5910 ?

Answer 20

not sure what you mean exactly

Answer 21

Nevermind lol, can you put the so far result in result in the equation format so I can be clear? The other one didn't show up when you posted.

Answer 22

here is how I would do it

Answer 23

\[\large \frac{ \frac{ 10 }{ x+1 } }{ 1/2 + \frac{ 3 }{ x+1} }\]

\[\large \frac{ 2(x+1)\frac{ 10 }{ x+1 } }{ 2(x+1)\frac{1}{2} + 2(x+1)\frac{ 3 }{ x+1} }\]

\[\large \frac{ 2*10 }{ x+1 + 2*3 }\]

\[\large \frac{ 2*10 }{ x+1 + 6 }\]

\[\large \frac{ 20 }{ x+7 }\]

Answer 24

So that would be the final answer?

Answer 25

How come you didn't multiply the 3/x+1 by the 2(x+1) ?

Answer 26

@jim_thompson5910

Answer 27

i did in a way, the x+1 in the denominator of 3/(x+1) cancels out with the x+1 in 2(x+1)

Answer 28

so

3/(x+1) times 2(x+1) = 3*2 = 6

Answer 29

Oh okay!

Answer 30

Oh I see now! Thanks so much ! :)

Answer 31

glad it's all making sense now