Question

me ajudem!!!
resolva as equação fracionarias:
a)$\frac{12}{2x-3}$=4
b)$\frac{5x+3}{x}$=2
c)$\frac{1}{4x}$+$\frac{1}{12}$=$\frac{2}{3x}$
d)$\frac{4}{3x}$-$\frac{x+4}{6x}$=2
e)$\frac{3}{x-1}+\frac{4x}{x+1}$=4

Answer 1

a)

$\frac{12}{2x-3}=4 \\ 8x-12=12\\ 8x=12+12 \\ 8x=24$

$x=\frac{24}{8} \\ x=3$

b)

$\frac{5x+3}{x}=2 \\ 5x+3=2x \\ 5x-2x=-3 \\ 3x=-3$

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

c)

$\frac{1}{4x}+\frac{1}{12}=\frac{2}{3x}$

$\frac{3+x=8}{12x} \\ x+3=8 \\ x=8-3 \\ x=5$

d)

$\frac{4}{3x}-\frac{x+4}{6x}=2$

$\frac{8-1(x+4)=12x}{6x} \\ 8-x-4=12x$

$12x+x=8-4 \\ 13x=4\\ x=\frac{4}{13}$

e)

$\frac{3}{x-1}+\frac{4x}{x+1}=4$

$\frac{3(x+1)+4x(x-1)=4(x+1)(x-1)}{(x-1)(x+1)}$

$3x+3+4{x}^{2}-4x=4{x}^{2}-4$

$-x=-3-4\\ -x=-7\times(-1)\\ x=7$