Question

6/x - 2/x-1 = 1/x+2 ; x is not equal to 0, 1, -2​

Answer 1

Answer:

(x−2)1+(x−1)2=x6

=(x−2)(x−1)x−1+2x−4=x6

=x(3x−5)=6(x−2)(x−1)

=3x2−5x=6(x2−x−2x+2)

=3x2−5x=6x2−18x+12

=13x−3x2−12=0

=3x2−13x+12=0

=3x2−4x−9x+12=0

=x(3x−4)−3(3x−4)=0

(3x−4)(x−3)

so, x=3 or x=34

Answer 2

$\frac{6}{x} - \frac{2}{ x - 1} = \frac{1}{x + 2}$

$\frac{6(x - 1) - 2(x)}{x(x - 1)} = \frac{1}{x + 2}$

$\frac{6x - 6 - 2x}{ {x}^{2} - 1 } = \frac{1}{x + 2}$

$\frac{4x - 6}{ {x}^{2} - 1} = \frac{1}{x + 2}$

$(4x - 6)(x + 2) = 1( {x}^{2} - 1)$

$4x(x + 2) - 6(x + 2) = {x}^{2} - 1$

$4 {x}^{2} + 8 - 6x - 12 = {x}^{2} - 1$

$= 4 {x}^{2} - {x}^{2} - 6x - 4 + 1$

$= 3 {x}^{2} - 6x - 3$

$= 3 {x}^{2} - (3 + 3)x - 3$

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

$= 3x(x - 1) - 3( x- 3)$

$= (3x - 3)(x - 3)$

$x = 3$