### Home > APCALC > Chapter 6 > Lesson 6.1.4 > Problem6-52

6-52.

Without a calculator, solve for $x$: $( \frac { 1 } { 1 + ( \frac { 5 } { x } ) ^ { 2 } } ) ( \frac { - 5 } { x ^ { 2 } } ) - ( \frac { 1 } { 1 + ( \frac { 1 } { x } ) ^ { 2 } } ) ( \frac { - 1 } { x ^ { 2 } } )=0$.

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There are many ways to solve this equation.

$\text{One method is to let }U=\frac{1}{x}\text{ and solve for }U\text{ first.}$

$x=\pm \sqrt{5}$