How do you solve $x/(x-3)=6/(x-3)$ ?

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Answer 1 · 2016-08-29T08:44:16

$x=+3, or +6$

$x/(x-3)=6/(x-3)$

i.e. $6(x-3)=x(x-3)$

$6x-18=x^2-3x$

$x^2-9x+18=0$

This is a quadratic in $x$ , for which we might use the quadratic formula. Alternatively we could factor it to give:

$(x-3)(x-6)=0$

Thus $x$ has roots at $+3$ or $+6$

How do you solve x/(x-3)=6/(x-3)x/(x-3)=6/(x-3)?