Question

equacoes fracionarias:
$a) \frac{70}{x} = \frac{315}{2x+5}$
$b) \frac{x}{x-2} + \frac{3}{x+2}= \frac{ x^{2}+1 }{ x^{2} -4}$
se for possivel me explique :)

Answer 1

a)
$\frac{70}{x} = \frac{315}{2x+5}$

multiplica cruzado

$315x=140x+350$

$315x-140x=350$

$x= \frac{350}{175}$

$\fbox{ x=2 }$

b)

$\frac{x}{x-2} + \frac{3}{x+2} = \frac{x^2+1}{x^2-1}$

mmc=x²-4  (x+2)(x-2)

$x(x+2)+3(x-2)=x^2+1$

$x^2+2x+3x-6=x^2+1$

$x^2+2x+3x-6-x^2-1=0$

cancela x² com -x²

$2x+3x=1+6$

$5x=7$

$\fbox{ x= \frac{7}{5} }$