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How do you add $\frac{a - 1}{a + 1} + \frac{a + 1}{a - 1}$ $(a-1)/(a+1 )+ (a+1)/(a-1)$ ?

1 Answer

Oct 2, 2015

Convert the denominators to a common value and simplify to get
$XXX \frac{2 (a^{2} + 1)}{a^{2} - 1}$ $color(white)("XXX")(2(a^2+1))/(a^2-1)$

Explanation:

$\frac{a - 1}{a + 1} + \frac{a + 1}{a - 1}$ $color(red)((a-1)/(a+1)) + color(blue)((a+1)/(a-1))$

$XXX = \frac{a - 1}{a + 1} \cdot \frac{a - 1}{a - 1} + (\frac{a + 1}{a - 1}) \cdot \frac{a + 1}{a + 1}$ $color(white)("XXX")=color(red)((a-1)/(a+1)) * (a-1)/(a-1) + (color(blue)(a+1)/(a-1)) * (a+1)/(a+1)$

$XXX = \frac{{(a - 1)}^{2} + {(a + 1)}^{2}}{(a - 1) (a + 1)}$ $color(white)("XXX")=(color(green)((a-1)^2)+color(brown)((a+1)^2))/((a-1)(a+1)$

$XXX = \frac{a^{2} - 2 a + 1 + a^{2} + 2 a + 1}{(a - 1) (a + 1)}$ $color(white)("XXX")=(color(green)(a^2-2a+1)+color(brown)(a^2+2a+1))/((a-1)(a+1))$

$XXX = \frac{2 (a^{2} + 1)}{a^{2} - 1}$ $color(white)("XXX")=(2(a^2+1))/(a^2-1)$

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