Hi all,

Below are several problems I believe I have set up and solved correctly but would like for others to review them as well.

1). x / x^2 - 3x - 18 multiplied by x^2 - x - 12 / x^2 - 4x

= x / (x - 6) (x + 3) multiplied by (x - 4) (x + 3) / x (x - 4)

= 1 / x - 6 <-- I never factored in a LCD to get this answer, simply reduced.

2). x^2 - 3x - 4 / x^2 - 16 multiplied by x +4 / 3x - 9

= (x - 4) (x + 1) / (x + 4) (x - 4) multiplied by x + 4 / 3 (x - 3)

= x + 1 / 3 (x - 3) <-- Again, no LCD was factored into the equation, simple reduction only.

3). x - 3 / x + 2 divided by x^2 - x - 6

= x - 3 / x + 2 multiplied by 1 / (x - 3) (x + 2)

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

4). 4 / x + 3 subtracted by 6 / 3x + 9

= 4 / x + 3 subtracted by 6 / 3 (x + 3); LCD equals 3 (x + 3)

= 3 (x + 3) times 4 / x + 3 subtracted by 6 / 3 (x + 3)

= 12 - 6 / 3 (x + 3) or 2 / x +3 when simplified

5). x + 3 / x^2 - x - 12 plus 2 / x +3 = 1 / x - 4

= x + 3 / (x - 4) (x + 3) plus 2 / x + 3 = 1 / x - 4; LCD = (x - 4) (x + 3)

= (x - 4) 2 = x + 3

= 2x - 8 = x + 3

2x = x + 11

x = 11

Is anyone able to verify that my equations are set up properly and with correct answers?

Thank you.