## Blondisaurus one year ago How would you go about solving this equation for x? (In comments)

1. Blondisaurus

$\frac{ x }{ x-3 } = \frac{ 3 }{ x-3 }+9$

2. amoodarya

$\frac{x}{x-3}=\frac{3}{x-3}+9\\$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

3. amoodarya

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

4. amoodarya

the equation has no root

5. amoodarya

or no solution

6. anonymous

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