Question

выполните действия
$\frac{a {}^{2} }{a {}^{2} { - 4}^{} } - \frac{a}{a + 2}$
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Answer 1

Пошаговое объяснение:

$\frac{a {}^{2} }{a {}^{2} -4 } - \frac{a}{a + 2} = \frac{a {}^{2} }{(a - 2) \times (a + 2)} - \frac{a}{a + 2} = \frac{a {}^{2} - a \times (a - 2) }{(a - 2) \times (a + 2)} = \frac{a {}^{2} - a {}^{2} + 2a }{a {}^{2} - 4} = \frac{2a}{a {}^{2} - 4 }$

Answer 2

Решение и ответ:

$\displaystyle \frac{{{a^2}}}{{{a^2}-4}}-\frac{a}{{a+2}}=\frac{{{a^2}}}{{{a^2}-{2^2}}}-\frac{a}{{a+ 2}}=\frac{{{a^2}}}{{\left( {a-2} \right)\left({a+2} \right)}}-\frac{a}{{a+2}}= \frac{{{a^2}}}{{\left( {a-2} \right)\left({a+2} \right)}}-\frac{{a\left({a-2} \right)}}{{\left({a+2} \right)\left({a-2}\right)}}=$$\displaystyle =\frac{{{a^2}-a\left( {a-2} \right)}}{{\left( {a+2} \right)\left({a-2} \right)}}= \frac{{{a^2} - {a^2}+2a}}{{\left({a+2} \right)\left( {a-2} \right)}}= \boxed{\frac{{2a}}{{\left({a+2} \right)\left( {a-2} \right)}}}$