Question

How would you go about solving this equation for x? (In comments)

Answer 1

\[\frac{ x }{ x-3 } = \frac{ 3 }{ x-3 }+9 \]

Answer 2

\[\frac{x}{x-3}=\frac{3}{x-3}+9\\\]first note that x cant be 3
now lets go \[\frac{x}{x-3}-\frac{3}{x-3}=9\\\frac{x-3}{x-3}=9\\x \neq 3\\we \\can\\simplify\\1=9\\\]
and it has no roots

Answer 3

another method

multiply by (x-3)
\[(x-3)(\frac{x}{x-3}=\frac{3}{x-3}+9)\\x=3+9(x-3)\\x-9x=-27+3\\-8x=-24\\x=3\]
but \[x \neq 3\\\]
because denominator goes to zero

Answer 4

the equation has no root

Answer 5

or no solution

Answer 6

it's simply like that 2=2+1, which is false equation. above is conditional equation with no solution.