Question

please help! I can't figure out the two x's in this equation because I'm not sure I can simplify it beforehand. The equation is in the comments...

Answer 1

\[\frac{ x }{ x-12 } = \frac{ 1 }{ x-1 }\]

Answer 2

"cross multiply" as they say, and start with
\[x(x-1)=x-12\]

Answer 3

then multiply out on the left to get
\[x^2-x=x-12\]

Answer 4

put all on one side of the equal sign by subtracting \(x\) and adding \(12\) and get
\[x^2-2x+12=0\] then try to factor or use the quadratic formula to solve for \(x\)

Answer 5

viola! standard form.

Answer 6

i think the problem is that the solutions are not real numbers

Answer 7

awesome! I get it from that part (: thank you so much!

and yes, it's a multiple choice question and the answers aren't real numbers. So it's fine!

Answer 8

oh in that case you should not set it equal to zero
leave it as
\[x^2-2x=-12\] complete the square via
\[(x-1)^2=-12+1=-11\] and get
\[x=1\pm\sqrt{11}i\] more quickly without formula

Answer 9

oh okay, thank you so much! I appreciate your help!

Answer 10

yw