1-2 – 8 = 3x = -9

x=-3

2. x/x+3=(6/x-3)+1

1+3 -1+3 = 6/x = 6

6/6 = x

x = 1

3. (3x^2)/(x+1)=2+(3x/x+1)

3x^2/(x+1) = 3 + 3+1 =7

3x^2 = 7x +7

3x^2 -7x -7 = 0

x= [7 +/- sqrt(49+84)]/6

You may have meant to write the equation as

(3x^2)/(x+1)=2+3x/(x+1)

(3x^2-3x)/(x+1) = 2

3x^2-3x = 2x +2

3x^2 -5x – 2 = 0

(3x+1)(x-2) = 0

x=2; x=-1

Substitute back in to check.

(3x^2)/(x+1)=2+3x/(x+1)

12/3=4=2+6/3=4 OK

x=-1 is not a solution since division by 0 is undefined. Therefore,

x=2

4 is truncated

5. x/(x^2-1)- (x+3)/(x^2-x)= – 3/(x^2+2x-3)

x/[(x+1)(x-1)] – (x+3)/[x(x-1)] = -3/[(x+3)(x-1)]

x/(x+1) – (x+3)/ x = -3/ (x+3)

x^2/[x(x+1)] – (x+3)(x+1)/[x(x+1)] = -3/(x+3)

(x^2 – x^2 -4x -3)[x(x+1)] = -3/(x+3)

(4x+3)/[x(x+1)] = 3/(x+3)

(4x+3)(x+3) = 3x(x+1)

4x^2+15x+9 = 3x^2+3x

x^2+12x+9 = 0

[x + -12 +/-sqrt(144-36)]

x = -6 +/-3sqrt(3)

Both values checked ok

6. truncated