SOLUTION: 2 / (y^2+y) - 2 / (xy+x) divided by 1 / (xy+x) - 1 / (y^2+y)

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Question 1129688: 2 / (y^2+y) - 2 / (xy+x) divided by 1 / (xy+x) - 1 / (y^2+y)
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!



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=%282x%28y%2B1%29+-+2y%28y%2B1%29+%29%2F%28y%28y%2B1%29+-+x%28y%2B1%29%29

=%28%282x+-+2y%29cross%28%28y%2B1%29+%29%29%2F%28%28y+-+x%29cross%28%28y%2B1%29%29%29

=%282x+-+2y%29%2F%28y+-+x%29

=-2cross%28%28y+-+x%29%29%2Fcross%28%28y+-+x%29%29

=-2



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The response from the other tutor shows a valid solution with correct algebraic steps.

However, the simplified form can be found FAR more easily if you take a moment to look at the original expression before you plunge into using standard algebraic processes.



>> The numerators of both fractions in the numerator are 2; the numerators of both fractions in the denominator are 1.
>> The denominators of the two fractions in the numerator and denominator are the same, but in opposite orders.

So make the orders of the denominators in both numerator and denominator the same, and make all the numerators of the individual fractions 1, by factoring a -2 out of the numerator:



Then it is clear that the simplified form is just "-2".