x(x+y)/x = ?

[Ys*]

Does the math below equate to condition one or two? I tried using special calculators but they didn't help me understand.

(Condition 1) x(x+y)/x => (x^2 + xy)/x => (x + y)

OR

(Condition 2)x(x+y)/x => 1(1 + y)/x => (1 + y)/x

 

[HallsofIvy]

Does the math below equate to condition one or two? I tried using special calculators but they didn't help me understand.

(Condition 1) x(x+y)/x => (x^2 + xy)/x => (x + y)

As long as x is not 0 (in which this would evaluate to 0/0 which is "undetermined") this is true.

OR

(Condition 2)x(x+y)/x => 1(1 + y)/x => (1 + y)/x

How did x become "1" in the numerator? a/a= 1 (for non-zero a) but a times a is not 1.

 

[Ys*]

I don't think you understand. This is algebra and I wanted to see if I'm following the rules correctly. I went over this with some friends yesterday and although it tricked us we found out.

(Condition 1) x(x+y)/x => (x^2 + xy)/x => (x + y)

When the teacher presented the solution he skipped a step and divided by x twice leading him to equate directly to "(1 + y)/x"

 

[HallsofIvy]

Every one here, except possibly you, understood what you were asking and answered correctly.