Question

4)determine os seguintes produtos
5)determine os seguintes quociente
6)n da pra escrever mas ta ai
7)aplicando a regra dos produtos notáveis desenvolva
8)resolva a equação 2x^2 - 2x-24=0 aplicando a faturação
9)sendo a e b numero reais positivos sabendo que nesta condições o valor de (a-b)^2 e
Ajuda ai familia so falta essas pra mim pfvrrr

Answer 1

Explicação passo-a-passo:

4)

a)

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

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

$\sf =\red{\dfrac{a-1}{a}}$

b)

$\sf \dfrac{x+y}{x-y}\cdot\dfrac{2y}{x+y}$

$\sf =\dfrac{(x+y)\cdot2y}{(x-y)\cdot(x+y)}$

$\sf =\red{\dfrac{2y}{x-y}}$

c)

$\sf \dfrac{3a}{a-b}\cdot\dfrac{a^2-b^2}{6ab}$

$\sf =\dfrac{3a\cdot(a+b)\cdot(a-b)}{(a-b)\cdot6ab}$

$\sf =\dfrac{3a\cdot(a+b)}{6ab}$

$\sf =\red{\dfrac{a+b}{2b}}$

d)

$\sf \dfrac{14x}{a^2-4}\cdot\dfrac{a+2}{7x}$

$\sf =\dfrac{14x\cdot(a+2)}{(a+2)\cdot(a-2)\cdot7x}$

$\sf =\dfrac{14x}{(a-2)\cdot7x}$

$\sf =\red{\dfrac{2}{a-2}}$

e)

$\sf \dfrac{ax+x}{x^2-y^2}\cdot\dfrac{3x-3y}{a+1}$

$\sf =\dfrac{x\cdot(a+1)\cdot3\cdot(x-y)}{(x+y)\cdot(x-y)\cdot(a+1)}$

$\sf =\red{\dfrac{3x}{x+y}}$

f)

$\sf \dfrac{3y+3}{x^4+x^2}\cdot\dfrac{x^3}{y+1}$

$\sf =\dfrac{3\cdot(y+1)\cdot x^3}{x^2\cdot(x^2+1)\cdot(y+1)}$

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

g)

$\sf \dfrac{(a^2+2ax+x^2)\cdot(m-n)}{(m^2-n^2)\cdot(a+x)}$

$\sf =\dfrac{(a+x)\cdot(a+x)\cdot(m-n)}{(m+n)\cdot(m-n)\cdot(a+x)}$

$\sf =\red{\dfrac{a+x}{m+n}}$

5)

a)

$\sf \dfrac{y}{x+2}\div\dfrac{y^2}{x^2-4}$

$\sf =\dfrac{y}{x+2}\cdot\dfrac{x^2-4}{y^2}$

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

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

$\sf =\red{\dfrac{x-2}{y}}$

b)

$\sf \dfrac{2x+2y}{x-y}\div\dfrac{4x+4y}{2}$

$\sf =\dfrac{2x+2y}{x-y}\cdot\dfrac{2}{4x+4y}$

$\sf =\dfrac{2\cdot(x+y)}{x-y}\cdot\dfrac{2}{4\cdot(x+y)}$

$\sf =\dfrac{2\cdot(x+y)\cdot2}{(x-y)\cdot4\cdot(x+y)}$

$\sf =\red{\dfrac{1}{x-y}}$

c)

$\sf \dfrac{3ax}{a^2-x^2}\div\dfrac{6x}{a+x}$

$\sf =\dfrac{3ax}{a^2-x^2}\cdot\dfrac{a+x}{6x}$

$\sf =\dfrac{3ax}{(a+x)\cdot(a-x)}\cdot\dfrac{a+x}{6x}$

$\sf =\dfrac{3ax\cdot(a+x)}{(a+x)\cdot(a-x)\cdot6x}$

$\sf =\dfrac{3ax}{(a-x)\cdot6x}$

$\sf =\dfrac{a}{(a-x)\cdot2}$

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

d)

$\sf \dfrac{a^2-25}{ab}\div\dfrac{2a+10}{a}$

$\sf =\dfrac{a^2-25}{ab}\cdot\dfrac{a}{2a+10}$

$\sf =\dfrac{(a+5)\cdot(a-5)}{ab}\cdot\dfrac{a}{2\cdot(a+5)}$

$\sf =\dfrac{(a+5)\cdot(a-5)\cdot a}{ab\cdot2\cdot(a+5)}$

$\sf =\dfrac{(a-5)\cdot a}{ab\cdot2}$

$\sf =\red{\dfrac{a-5}{2b}}$

e)

$\sf \dfrac{4a}{b+1}\div\dfrac{8a^2}{2b+2}$

$\sf =\dfrac{4a}{b+1}\cdot\dfrac{2b+2}{8a^2}$

$\sf =\dfrac{4a}{b+1}\cdot\dfrac{2\cdot(b+1)}{8a^2}$

$\sf =\dfrac{4a\cdot2\cdot(b+1)}{(b+1)\cdot8a^2}$

$\sf =\dfrac{4a\cdot2}{8a^2}$

$\sf =\dfrac{8a}{8a^2}$

$\sf =\red{\dfrac{1}{a}}$

f)

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

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

$\sf =\dfrac{(x-1)\cdot(x-1)}{2x\cdot(x+2)}\cdot\dfrac{4x}{x-1}$

$\sf =\dfrac{(x-1)\cdot(x-1)\cdot4x}{2x\cdot(x+2)\cdot(x-1)}$

$\sf =\dfrac{(x-1)\cdot4x}{2x\cdot(x+2)}$

$\sf =\dfrac{(x-1)\cdot2}{x+2}$

$\sf =\red{\dfrac{2x-2}{x+2}}$

g)

$\sf \dfrac{4+4a+a^2}{1-b^2}\div\dfrac{a^2-4}{b+1}$

$\sf =\dfrac{4+4a+a^2}{1-b^2}\cdot\dfrac{b+1}{a^2-4}$

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

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

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

8)

$\sf 2x^2-2x-24=0$

$\sf 2x^2+6x-8x-24=0$

$\sf 2x\cdot(x+3)-8\cdot(x+)=0$

$\sf (x+3)\cdot(2x-8)=0$

• $\sf x+3=0$

$\sf \red{x'=-3}$

• $\sf 2x-8=0$

$\sf 2x=8$

$\sf x=\dfrac{8}{2}$

$\sf \red{x"=4}$

O conjunto solução é S = {-3, 4}