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\left(\frac{x+2}{\left(x-2\right)\left(x+2\right)}+\frac{x-2}{\left(x-2\right)\left(x+2\right)}\right)x
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and x+2 is \left(x-2\right)\left(x+2\right). Multiply \frac{1}{x-2} times \frac{x+2}{x+2}. Multiply \frac{1}{x+2} times \frac{x-2}{x-2}.
\frac{x+2+x-2}{\left(x-2\right)\left(x+2\right)}x
Since \frac{x+2}{\left(x-2\right)\left(x+2\right)} and \frac{x-2}{\left(x-2\right)\left(x+2\right)} have the same denominator, add them by adding their numerators.
\frac{2x}{\left(x-2\right)\left(x+2\right)}x
Combine like terms in x+2+x-2.
\frac{2xx}{\left(x-2\right)\left(x+2\right)}
Express \frac{2x}{\left(x-2\right)\left(x+2\right)}x as a single fraction.
\frac{2x^{2}}{\left(x-2\right)\left(x+2\right)}
Multiply x and x to get x^{2}.
\frac{2x^{2}}{x^{2}-2^{2}}
Consider \left(x-2\right)\left(x+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{2x^{2}}{x^{2}-4}
Calculate 2 to the power of 2 and get 4.
\left(\frac{x+2}{\left(x-2\right)\left(x+2\right)}+\frac{x-2}{\left(x-2\right)\left(x+2\right)}\right)x
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and x+2 is \left(x-2\right)\left(x+2\right). Multiply \frac{1}{x-2} times \frac{x+2}{x+2}. Multiply \frac{1}{x+2} times \frac{x-2}{x-2}.
\frac{x+2+x-2}{\left(x-2\right)\left(x+2\right)}x
Since \frac{x+2}{\left(x-2\right)\left(x+2\right)} and \frac{x-2}{\left(x-2\right)\left(x+2\right)} have the same denominator, add them by adding their numerators.
\frac{2x}{\left(x-2\right)\left(x+2\right)}x
Combine like terms in x+2+x-2.
\frac{2xx}{\left(x-2\right)\left(x+2\right)}
Express \frac{2x}{\left(x-2\right)\left(x+2\right)}x as a single fraction.
\frac{2x^{2}}{\left(x-2\right)\left(x+2\right)}
Multiply x and x to get x^{2}.
\frac{2x^{2}}{x^{2}-2^{2}}
Consider \left(x-2\right)\left(x+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{2x^{2}}{x^{2}-4}
Calculate 2 to the power of 2 and get 4.