Question

resolva as equações
2)3/x-1/2=7/x

3)2+1/2=7/X

4)9/x+6/x=3

5)8-3/x=1/x

6)3/x+1/4=2/X

7)1/2x+3/8=2/x

8)x+1/3x+1/x=2/3

9)3/4x-3/5x+1/10=0

10)4x+5/8x-3/4=1-x/2x

Answer 1

$2)\\ \\ \frac{3}{x} -\frac{1}{2} =\frac{7}{x} \\ \\ mmc=2x\\ \\ \frac{6-x=14}{2x} \\ \\ 6-x=14\\ \\ -x=14-6\\ \\ -x=8.(-1)\\ \\ x=-8$

$3)\\ \\ 2+\frac{1}{2} =\frac{7}{x} \\ \\ mmc=2x\\ \\ \frac{4x+x=14}{2x} \\ \\ 4x+x=14\\ \\ 5x=14\\ \\ x=\frac{14}{5}$

$4)\\ \\ \frac{9}{x} +\frac{6}{x} =3\\ \\ mmc=x\\ \\ \frac{9+6=3x}{x} \\ \\ 3x=9+6\\ \\ 3x=15\\ \\ x=\frac{15}{3} \\ \\ x=5$

$5)\\ \\ 8-\frac{3}{x} =\frac{1}{x} \\ \\ mmc=x\\ \\ \frac{8x-3=1}{x} \\ \\ 8x-3=1\\ \\ 8x=1+3\\ \\ 8x=4\\ \\ x=\frac{4}{8} =\frac{1}{2}$

$6)\\ \\ \frac{3}{x} +\frac{1}{4} =\frac{2}{x} \\ \\ mmc=4x\\ \\ \frac{12+x=8}{4x} \\ \\ 12+x=8\\ \\ x=8-12\\ \\ x=-4$

$7)\\ \\ \frac{1}{2} +\frac{3}{8} =\frac{2}{x} \\ \\ mmc=8x\\ \\ \frac{4x+3x=16}{8x} \\ \\ 4x+3x=16\\ \\ 7x=16\\ \\ x=\frac{16}{7}$

$8)\\ \\ \frac{x+1}{3x} +\frac{1}{x} =\frac{2}{3} \\ \\ mmc=3x\\ \\ \frac{x+1+3=2x}{3x} \\ \\ x+1+3=2x\\ \\ 2x-x=1+3\\ \\ x=4$

$9)\\ \\ \frac{3}{4x} -\frac{3}{5x} +\frac{1}{10} =0\\ \\ mmc=20x\\ \\ \frac{15-4+2x=0}{20x} \\ \\ 15-4+2x=0\\ \\ 2x=-15+4\\ \\ 2x=-11\\ \\ x=-\frac{11}{2}$

$10)\\ \\ 4x+\frac{5}{8x} -\frac{3}{4} =\frac{1-x}{2x} \\ \\ mmc=8x\\ \\ \frac{32x^{2}+5-6x=4-4x}{8x} \\ \\ 32x^{2} +5-6x=4-4x\\ \\ 32x^{2} -6x+4x+5-4=0\\ \\ 32x^{2} -2x+1=0$

Δ = b² - 4.a.c

Δ = 4 - 4.32.1

Δ = 4 - 128

Δ = - 124

Delta negativo: raiz não existe em R