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\left(\frac{5}{5}+\frac{4}{5}\right)x=x+x
Convert 1 to fraction \frac{5}{5}.
\frac{5+4}{5}x=x+x
Since \frac{5}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.
\frac{9}{5}x=x+x
Add 5 and 4 to get 9.
\frac{9}{5}x=2x
Combine x and x to get 2x.
\frac{9}{5}x-2x=0
Subtract 2x from both sides.
-\frac{1}{5}x=0
Combine \frac{9}{5}x and -2x to get -\frac{1}{5}x.
x=0
Product of two numbers is equal to 0 if at least one of them is 0. Since -\frac{1}{5} is not equal to 0, x must be equal to 0.