Question

Resolver as equações fracionárias: a) x +1/x = 5/2
b) x/3 - 9/x = -2
c) x + 3/x-2 = 6
d) x + 1/x-4 = 6
e) x + 1/x-5 = 7

Answer 1

a)

$\frac{x+1}{x} =\frac{5}{2}$

5x = 2.(x + 1)

5x = 2x + 2

5x - 2x = 2

3x = 2

$x=\frac{2}{3}$

b)

$\frac{x}{3} -\frac{9}{x} =-2$

mmc = 3x

$\frac{x^{2}-27=-6x}{3x}$

x² + 6x - 27 = 0

c)

$x+\frac{1}{x-4} =6$

mmc = x - 4

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

x² - 4x + 1 = 6x - 24

x² - 4x - 6x + 1 + 24 = 0

x² - 10x + 25 = 0

d)

$\frac{x+1}{x-4} =6$

6(x-4) = x + 1

6x - 24 = x + 1

6x - x = 1 + 24

5x = 25

x = 25/5

x = 5

e)

$\frac{x+1}{x-5} =7$

7.(x-5)=x+1

7x - 35 = x + 1

7x - x = 1 + 35

6x = 36

x = 36/6

x = 6