Question

Виконайте дії:
(a - 2)/(a ^ 2 - 4) - (a - 2)/(4 - a ^ 2)
(15x - 2)/(10x ^ 2) + (5 + x)/(5x ^ 3)
7/(x ^ 2 + x) + 13/(x + 1)

Answer 1

Ответ:

$\dfrac{a-2}{a^2-4} -\dfrac{a-2}{4-a^2} =\dfrac{2}{a+2}$

$\dfrac{15x-2}{10x^2} +\dfrac{5+x}{5x^3} =\dfrac{3x^2+2}{2x^3}$

$\dfrac{7}{x^2+x}+\dfrac{13}{x+1} =\dfrac{7+13x}{x^2+x}$

Решение:

1)

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

$=\dfrac{2(a-2)}{a^2-2^2} =\dfrac{2(a-2)}{(a-2)(a+2)} =\boxed{\dfrac{2}{a+2}}$

2)

$\dfrac{15x-2}{10x^2} +\dfrac{5+x}{5x^3} =\dfrac{(15x-2)\cdot x}{10x^3} +\dfrac{(5+x)\cdot2}{10x^3}=$

$=\dfrac{15x^2-2x}{10x^3} +\dfrac{10+2x}{10x^3} =\dfrac{15x^2-2x+10+2x}{10x^3} =$

$=\dfrac{15x^2+10}{10x^3} =\dfrac{5(3x^2+2)}{10x^3} =\boxed{\dfrac{3x^2+2}{2x^3}}$

3)

$\dfrac{7}{x^2+x}+\dfrac{13}{x+1} =\dfrac{7}{x^2+x}+\dfrac{13x}{x(x+1)} =$

$=\dfrac{7}{x^2+x}+\dfrac{13x}{x^2+x} =\boxed{\dfrac{7+13x}{x^2+x} }$