Question 1129688
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The response from the other tutor shows a valid solution with correct algebraic steps.<br>
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.<br>
{{{(2 / (y^2+y) - 2 / (xy+x)) / (1 / (xy+x) - 1 / (y^2+y))}}}<br>
>> 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.<br>
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:<br>
{{{(-2(1 / (xy+x) - 1 / (y^2+y))) / ((1 / (xy+x) - 1 / (y^2+y)))}}}<br>
Then it is clear that the simplified form is just "-2".