Question

Trying to get rid of points. 99pts.

Perform the indicated operations: (2/x-2)+(x/x+9)-(x+20/x^2+7x-18)

Answer 1

for x<>2, (x+1)/(x+9)

Explanation:

cheatin' a lil as i saw OP's ans already ;)

the confusion was the Q should be:

2/(x-2) + x/(x+9) - (x+20)/(x^2+7x-18)

=(2(x+9) + x(x-2))/(x-2)(x+9) - (x+20)/(x-2)(x+9)

=(2x+18+x^2-2x-x-20)/(x+2)(x-9)

=(x^2-x-2)/(x-2)(x+9)

=(x-2)(x+1)/(x-2)(x+9)

for x<>2

=(x+1)/(x+9)

Answer 2

The answer is -2(4x^3+5x^2-x+20)/x^2

I mis-read the question. The answer should be (x+1)/(x+9)

Explanation:

(2/x-2)+(x/x+9)-(x+20/x^2+7x-18)

= 2/x-2+1+9-(20/x^2+8x-18)

=2/x+8-(20+8x^3-18x^2)/x^2

=(2x+8x^2-20-8x^3-18x^2)/x^2

=(-8x^3-10x^2+2x-20)/x^2

=-2(4x^3+5x^2-x+20)/x^2

I mis-read the question and it should be:

(2/(x-2))+(x/(x+9))-(x+20)/(x^2+7x-18)

=(2(x+9)+x(x-2) / (x-2)(x+9) - (x+20) / (x-2)(x+9)

=(2x+18+x^2-2x-x-20) / (x-2)(x+9)

=(x^2-x-2) / (x-2)(x+9))

= (x+1)(x-2) / (x-2)(x+9))

=(x+1)/(x+9)