If (x)/(4)2=4(x)/(2), then x=

1990 AMC 12 Problem 1

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\dfrac{\frac{x}{4}}{2}=\dfrac4{\frac{x}{2}},

then

x=

\pm\frac12

\pm1

\pm2

\pm4

\pm8

Simplify both complex fractions first

After clearing denominators, solve the resulting equation in

x^2

The equation simplifies to

\frac{x}{8}=\frac8x.

Since

x\ne0,

multiplying by

8x

gives

x^2=64,

x=\pm8.

Thus the correct answer is E.