Question

how do you solve for x in \frac{1}{2(x-1)}=5+\frac{3}{x-1}

Answer 1

\[\frac 12 (x - 2) = 5 + \frac 3{x-1}\]
is that the question?

Answer 2

yes that is the question

Answer 3

okay...first multiply all terms by 2..what do you get?

Answer 4

\[\frac{ 2 }{ 2(x-1)? }=10+\frac{6}{2(x-1)}

Answer 5

yes that is right... except for one minor mistake \[\frac 22(x-2) = 10 + \frac{6}{x-1}\]
do you see where you went wrong?

Answer 6

i didn't multiply the negative 1 by 2. wouldn't i also multiply the x-1 by 2 as well

Answer 7

no...remember i said multiply 2 to every term. 3/(x-1) is just one term so you multiply 2 to it only once. so you have \[\implies \frac 3{x-1} \times 2 \implies \frac 6{x-1}\]
make sense?

Answer 8

yes

Answer 9

wonderful. so do you now get how i got \[\frac 22 (x-2) = 10 + \frac 6{x-1}\]

Answer 10

yes

Answer 11

good. you can still simplify 2/2

Answer 12

which would equal 1