Question

efetue as seguintes adições e subtrações,considerando as condições de existência

Answer 1

Explicação passo-a-passo:

a)

$\sf \dfrac{x-1}{2-a}+\dfrac{x+1}{2+a}$

$\sf =\dfrac{(x-1)\cdot(2+a)+(x+1)\cdot(2-a)}{(2-a)\cdot(2+a)}$

$\sf =\dfrac{2x+ax-2-a+2x-ax+2-a}{2^2-a^2}$

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

$\sf =\red{\dfrac{4x-2a}{4-a^2}}$

b)

$\sf \dfrac{3p-q}{x^2-1}+\dfrac{3p+q}{x^2+2x+1}$

$\sf \dfrac{3p-q}{(x-1)\cdot(x+1)}+\dfrac{3p+q}{(x+1)\cdot(x+1)}$

$\sf =\dfrac{(3p-q)\cdot(x+1)+(3p+q)\cdot(x-1)}{(x-1)\cdot(x+1)\cdot(x+1)}$

$\sf =\dfrac{3px+3p-qx-q+3px-3p+qx-q}{(x^2-1)\cdot(x+1)}$

$\sf =\dfrac{3px+3px+3p-3p-qx+qx-q-q}{x^3+x^2-x-1}$

$\sf =\red{\dfrac{6px-2q}{x^3+x^2-x-1}}$

c)

$\sf x+2-\dfrac{x+2}{x^2-2x+1}$

$\sf \dfrac{(x+2)\cdot(x^2-2x+1)-(x+2)}{x^2-2x+1}$

$\sf =\dfrac{x^3-2x^2+x+2x^2-4x+2-x-2}{x^2-2x+1}$

$\sf =\dfrac{x^3-2x^2+2x^2+x-4x-x+2-2}{x^2-2x+1}$

$\sf =\red{\dfrac{x^3-4x}{x^2-2x+1}}$

d)

$\sf \dfrac{3-a}{3+a}-\dfrac{1+a}{9-a^2}-\dfrac{1-a}{3-a}$

$\sf =\dfrac{3-a}{3+a}-\dfrac{1+a}{(3-a)\cdot(3+a)}-\dfrac{1-a}{3-a}$

$\sf =\dfrac{(3-a)\cdot(3-a)-(1+a)-(1-a)\cdot(3+a)}{(3-a)\cdot(3+a)}$

$\sf =\dfrac{9-3a-3a+a^2-1-a-3-a+3a+a^2}{3^2-a^2}$

$\sf =\dfrac{a^2+a^2-3a-3a+3a-a-a+9-1-3}{9-a^2}$

$\sf =\red{\dfrac{2a^2-5a+5}{9-a^2}}$