Simplify this equation...?

Question

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

Thanks but I need an answer, not criticism.

Answer 1

common denominator is x(x-2)² multiply top and bottom by the missing factors for each fraction

2(x-2)² + x(x-2) +3(x) ...... 2x²-8x+8 +x²-2x +3x
------------------------------ = ---------------------------
x(x-2)² ................................. x(x-2)²

3x²-7x+8
------------
x(x-2)²

Answer 2

The LCM (Lease Common Multiple) of the denominators of the given fractions = x(x-2)^2
So, multiply and divide throughout by (x-2)^2 and that yields:

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

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

Let's simplify each term separately:

2*(x-2)^2 = 2*(x^2 - 4x + 4) = 2x^2 - 8x + 8

1x(x-2) = x^2 - 2x

Put these in the main expression:
(2x^2 - 8x + 8 + x^2 - 2x + 3x)/x(x-2)^2
= (3x^2 - 7x + 8)/x(x-2)^2

Answer 3

2 / x + 1 / (x - 2) + 3 / (x - 2) ²
[2 (x - 2) ² + (x )(x - 2) + 3 x ] / [(x) (x - 2) ² ] = N / D
N = 2(x ² - 4x + 4) + x ² - 2x + 3x
N = 2 x ² - 8x + 8 + x ² - 2x + 3x
N = 3 x ² - 7x + 8
D = (x) (x - 2) ²
N / D = (3 x ² - 7x + 8) / [ (x) (x - 2) ² ]

Answer 4

What good will a bunch of answers do? Maybe you should show us your work and ask if it's right or something. If you just want answers, look for the answers to the odd numbered problems in the back of the book. If you need answers for a class, won't your teacher want to see your work, not just the answers? I'm a former math teacher and I know that I would.

Answer 5

I agree with Robert B, its one thing if you get stuck on a hard problem and come on here and ask, its another if you put all your homework on here and expect people to do it for you. Maybe if you wouldn't cheat like this you'd know how to do these problems and wouldnt need our help.