How do you solve x/(x-3)=2-2/(x-3)?
1 Answer
The solution is
Explanation:
In an equality you have that the left side of the
In this case
\frac{x}{x-3}=2-\frac{2}{x-3}
we start multiplying left and right for
(x-3)\frac{x}{x-3}=(x-3)\left(2-\frac{2}{x-3}\right)
(x-3)\frac{x}{x-3}=2(x-3)-(x-3)\frac{2}{x-3}
we simplify the
x=2(x-3)-2
x=2x-6-2
x=2x-8
now we add left and right $-2x$
x-2x=2x-2x-8
-x=-8
and finally we multiply for
-1(-x)=-1(-8)
x=8.
In order to verify if our result is correct we substitute it in the initial equation and we must obtain an identity.
\frac{x}{x-3}=2-\frac{2}{x-3}
\frac{8}{8-3}=2-\frac{2}{8-3}
\frac{8}{5}=2-\frac{2}{5}
\frac{8}{5}=\frac{2\times 5-2}{5}
\frac{8}{5}=\frac{10-2}{5}
\frac{8}{5}=\frac{8}{5}
so we are sure that our solution is correct.