algebraic fractions help please!?

Question

how would i solve:

6/x-2 - 6/x+1 = 1

thank you!

Answer 1

6.(x + 1) - 6.(x - 2) = (x - 2).(x + 1)
,

6x + 6 - 6x + 12 = x² - x - 2

18 = x² - x - 2

x² - x - 20 = 0

(x - 5).(x + 4) = 0

sox = 5,

and x = - 4

Answer 2

if you mulitlpy the whole eq. by x-2 it becomes

6 - (6(x-2)/(x+1)) = x-2 (RHS - Because 1 x (x-2) = x-2)

then multiply by (x+1) so

6(x+1) - 6(x-2) = (x-2)(x+1) then expand brackets and simplify

6x + 6 - 6x + 12 = x^2 - x -2

x^2 - x - 20 = 0 complete the square

(x-5)(x+4) = 0 so x=5 or x= -4

check in original equation

x=5 6/3 - 6/6 = 1 correct

x= -4 6/-6 - 6/-3 = 1 correct

Answer 3

6.(x + 1) - 6.(x - 2) = (x - 2).(x + 1)
6x + 6 - 6x + 12 = x² - x - 2
18 = x² - x - 2
x² - x - 20 = 0
(x - 5).(x + 4) = 0
x = 5, x = - 4

Answer 4

sure there are not supposed to be any parentheses in that equation, the way it looks, like -1=1, as Spock would say Illogical, he he, do you mean (6/(x-2)) - (6/(x+1)) = 1 ?

Answer 5

Multiply everything by (x-2) and then by (x+1). Then, solve like any other quadratic! :)

Answer 6

make both denominators equal to (x+1)(x-2)