Question

resolva as questões ​

Answer 1

a) $\frac{2}{2x-1}=\frac{5}{x+1}$

$2(x+1)=5(2x-1)$

$2x+2=10x-5$

$2x-10x=-5-2$

$-8x=-7$

$8x=7$

$x=\frac{7}{8}$

b) $\frac{x}{x-1}+\frac{x-1}{x+1}=2$

$\frac{x(x+1)}{(x-1)(x+1)}+\frac{(x-1)(x-1)}{(x+1)(x-1)}=2$

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

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

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

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

$-x+1=-2$

$-x=-2-1$

$-x=-3$

$x=3$