Question

1- Resolva as equações fracionárias:

a) x+1/x-3= 5                  sendo U = IR - {3}

b) x+10/2=4x-2/x-2          sendo U = IR - {2}

Me ajudem!!! obrigado 

Answer 1

a)

$\frac{x+1}{x-3} =5$

multiplica cruzado

$5(x-3)=x+1$

$5x-15=x+1$

$5x-x=1+15$

$4x=16$

$x= \frac{16}{4}$

x=4

S={4}

b)

$\frac{x+10}{2} = \frac{4x-2}{x-2}$

$(x+10)(x-2)=2(4x-2)$

$x^{2} -2x+10x-20=8x-4$

$x^{2} +8x-8x=-4+20$

$x^{2} =16$

$x= \sqrt{16}$

x= ± 4

S={-4,4}

Answer 2

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, $x=\pm4$.

$S=\{-4, 4\}$