Question

Help me please solve this rational expression?

(1/3+x) + (1/x) = (1/2)

Answer 1

Here is the original word problem:

Answer 2

i posted the same thing about 25 minutes ago and for some reason no one could solve.. so.. o.o

Answer 3

\[\frac{ 1 }{ t+3 }+\frac{ 1 }{t }=\frac{ 1 }{2 }\]
\[\frac{ t+t+3 }{t \left( 1+t \right) }=\frac{ 1 }{ 2 }\]
\[2\left( 2t+3 \right)=t ^{2}+t,t ^{2}+t-4t-6=0,~t ^{2}-3t-6=0\]
solve it.

Answer 4

Woah. o.o What's that bottom part. o.e

Answer 5

correction ,write 3+t in place of 1+t

Answer 6

I'm confused. I'm not supposed to simplify here. I'm finding an actual numerical value.

Answer 7

WHO CAME UP WITH THE EXPRESSION?

Answer 8

I HAVE NO IDEA. stupid common core.. @nincompoop

Answer 9

OKAY

Answer 10

I've seen it solved before. Somehow, the x needs to get isolated but I don't know how to do that with rational expressions.

Answer 11

\[4t+6=3t+t ^{2},t ^{2}-t-6=0\]

Answer 12

\[t ^{2}-3t+2t-6=0,t \left( t-3 \right)+2\left( t-3 \right)=0\]
\[\left( t-3 \right)\left( t+2 \right)=0,t=3,t=-2\]
rejecting t=-2
t=3

Answer 13

OH, thank you!

Answer 14

So if I plugged 3 into the original equation, it should satisfy?

Answer 15

you are correct.

Answer 16

thank you!

Answer 17

\[\frac{ 1 }{6 }+\frac{ 1 }{3 }=\frac{ 1+2 }{ 6 }=\frac{ 3 }{6 }=\frac{ 1 }{ 2 }\]

Answer 18

np

Answer 19

So the expression above, it simplifies to 2(2t+3)? this one: x+x+3/x(3+t)

Answer 20

i mean 2x. My teacher doens't like it when I use anything other than x, y or z lol

Answer 21

I have used t only because it is time.Otherwise you can use any variable x,y,z,a,b,...etc.

Answer 22

But that's what it simplifies to?

Answer 23

Nvm, got it! Thanks!