Question

3. Resolva as seguintes equaçoes fracionarias do 2 grau abaixo
A. x+1/x-5=7

B. y+3/y-1=y+1/3

C. x+1/x-3=5

D. x+1/x=10/3

Alguem pode me ajudar por favor...

Answer 1

Resposta:

$A)\\ \\ \frac{x+1}{x-5}=7\\ \\ mmc=x-5\\ \\\frac{x+1=7x-35}{x-5}\\ \\ despreze~o~denominador\\ \\ x+1=7x-35\\ \\ 7x-x=1+35\\ \\ 6x=36\\ \\ x=\frac{36}{6}\\ \\ x=6$

$B)\\ \\ \frac{y+3}{y-1}=\frac{y+1}{3}\\ \\3(y+3)=(y+1)(y-1)\\ \\3y+9=y^{2}-1\\ \\ y^{2}-3y-1-9=0\\ \\ y^{2}-3y-10=0\\ \\delta=b^{2}-4.a.c\\ \\delta=(-3)^{2}-4.1.(-10)\\ \\ delta=9+40=49\\ \\ y=\frac{-b+-\sqrt{delta}}{2.a} \\ \\ y=\frac{3+-\sqrt{49}}{2} \\ \\y=\frac{3+-7}{2} \\ \\ y'=\frac{3+7}{2} =\frac{10}{2} =5\\ \\ y''=\frac{3-7}{2} =-\frac{4}{2} =-2\\ \\ S~~(y'=5~~y''=-2)$

$C)\\ \\ \frac{x+1}{x-3}=5\\ \\ mmc=x-3\\ \\ \frac{x+1=5x-15}{x-3} \\ \\ despreze~o~denominador\\ \\ x+1=5x-15\\ \\ 5x-x=1+15\\ \\ 4x=16\\ \\ x=\frac{16}{4}\\ \\ x=4$

$D)\\ \\ \frac{x+1}{x}=\frac{10}{3} \\ \\ 10x=3(x+1)\\ \\ 10x=3x+3\\ \\ 10x-3x=3\\ \\ 7x=3\\ \\ x=\frac{3}{7}$