why in the equation (x^2-3x)/(x^2+1)=2 can't i cross out the x^2s to get -3x/1=2 (ofc without the x it doesnt make sense but logically cant you cross the identical numerator and denominator parts out)?
+130513 We could only do that if we had this :
[x^2 * -3x] / [x^2 * 1 ] = 2 → -3x = 2
To see why we can't do what you suggest....let's look at this, instead
[7 - 2] / [ 7 + 5] if we "crossed out" the "7s" ??? ....we would end up with -2/5
But.......
[7 - 2] / [7 + 5] = 5/12 and that's not -2/5
Thus....the rule is....we can cancel multiplication on top and bottom, but not addition/subtraction
Does that make sense ???
Plus....look at what would be your solution....x = -2/3....see if that works in the original problem.....[it won't !!! ]
