Short expression x2−y2x(x−y)+x2−y2x(x+y)I tried to short this expression: x2−y2x(x−y)+x2−y2x(x+y)The result should be 2 but I get:x2−y2x2−xy+x2−y2x2+xy=y2yx+−y2yx=0What did I do wrong?

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Tristatex9tw · Accepted Answer

Don&#039;t know how you got from ²²²x²−y²x²−yx to y2xybut fractions just don&#039;t work that way. To add those, you need a common denominator. Here you could use x(x−y)(x+y), but it&#039;s a lot faster to note that x2−y2=(x+y)(x−y) and then simplify both fractions so that they get common denominator x.

Cassius Villarreal · Accepted Answer

You did not find a common denominator before adding the fractions since x2−xy≠x2+xy. Moreover, you cannot add fractions &#039;top to bottom&#039;, that is 23+14≠37this is why we find the common denominator. Try finding the common denominator first, it will be ....x(x−y)(x+y)and then adding your fractions.

Short expression \(\displaystyle{\frac{{{x}^{{2}}-{y}^{{2}}}}{{{x}{\left({x}-{y}\right)}}}}+{\frac{{{x}^{{2}}-{y}^{{2}}}}{{{x}{\left({x}+{y}\right)}}}}\) I tried to short this

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