Did I do these right? There about SIMPLIFYING rational expressions?

Question

1.x/x+xy=x/xy
2. 3x^2+6x/3x^2+9x=1x+2/1x+3
3.x^2+2x+1/x+1=1
4.x^2+3x-18/2x-6=x+9/x-3
5.2x^2-4x-6/x-3=2x-3/x-3

Answer 1

1.x/x+xy=?x/xy?

using x as common denom

(x+ x²y) / x =
factor out an x
x(1+xy) / x =
cancel the top & bottom x to get
1+xy

2. 3x² +6x/3x²+9x=?1x+2/1x+3?
factor out 3x in the numerator & denominator then cancel them out like this:

3x (x +2) / 3x( x + 3)
(x +2) / ( x + 3) , You got this one right, the 1 is understood to be there, so no need to write it. 10 points.

3. x² +2x+1/x+1=?1?
The first 2 terms and the last can be factored:
x² +2x+1/x+1=
x² +2x+1+1/x=
(x+1)² +1/x =
find common denominator
[x(x+1)² +1] / x

4.[x² + 3x -18 ]/ [2x-6] =?x+9/x-3?
factor top & bottom
[ (x+6)(x-3) ]/ [2(x-3)]
cancel the x-3 terms
(x+6) / 2

5. (2x² - 4x - 6) / (x-3) =?2x-3/x-3?
2(x² - 2x - 3) / (x-3) =
[2(x-3)(x+1)] / (x-3) =
the x-3 terms cancel, leaving
2(x+1)

Answer 2

No,
1.x/x+xy=1+xy i.e. x divided by x equal to 1
2.(3x^2+6x)/(3x^2+9x)=(x+2)/(x+3)
3.(x^2+2x+1)/(x+1)=x+1
4.(x^2+3x-18)/(2x-6)=(x+6)/2
5.(2x^2-4x-6)/(x-3)=2(x+2)
note that brackets are very important so you must include them in your answers

Answer 3

yes