Question

1-Resolva as seguintes equações fracionarias

A) x-2/x = x+1/x+3, U=R* -{-2}

Answer 1

a) \dfrac{x+1}{x-3}=5
Temos que, x+1=5(x-3)
x+1=5x-15
5x-x=1+15
Deste modo, 4x=16 e x=\dfrac{16}{4}=4
S=\{4\}.
b) \dfrac{x+10}{2}=\dfrac{4x-2}{x-2}
(x+10)(x-2)=2(4x-2)
x^2+8x-20=8x-4
Assim, x^2=20-4=16, ou seja, x=\pm\sqrt{16}.
Logo, x=\pm4.
S=\{-4, 4\}