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write 4/x+2 + 3/x-2 as a single fraction in its simplest form

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[tex]\frac{4}{x+2}^{(x-2}+ \frac{3}{x-2} ^{(x+2}= \\\\ = \frac{4(x-2)+3(x+2)}{(x-2)(x+2)}= \\\\ =\frac{4x-8+3x+6}{x^2-4}= \\\\ =\boxed{\frac{7x-2}{x^2-4}}[/tex]
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