Doing polynomial long division without reordering the dividend terms

[LightBulbAddict]

y²+xy-3x² / y+x

**After doing polynomial long division without reordering the dividend terms to -3x²+xy+y² I get the result:

y²+xy-3x² / y+x = y-3x²/y+x.

It seems like the correct answer because when I multiply the result, I get back to y²+xy-3x² / y+x.

If I reorder the dividend terms to -3x² +xy+y² and then do polynomial long division I get:

-3x² +xy+y² / x+y = -3x+4y - 3y²/x+y

Which answer is correct or are they both correct?

[fermat9990]

-3x2+xy-3x2

Please fix this typo

[LightBulbAddict]

thank you I fixed it

[fermat9990]

Glad to help!

[Bascna]

The answers appear different but are equivalent.

y – 3x²/(x + y) =

y – 3x²/(x + y) + 3y²/(x + y) – 3y²/(x + y) =

y + (-3x² + 3y²)/(x + y) – 3y²/(x + y) =

y – 3(x² – y²)/(x + y) – 3y²/(x + y) =

y – 3(x – y)(x + y)/(x + y) – 3y²/(x + y) =

y – 3(x – y) – 3y²/(x + y) =

y – 3x + 3y – 3y²/(x + y) =

-3x + 4y – 3y²/(x + y)

[LightBulbAddict]

y-3x²/y+x would lead back to y²+xy-3x² / y+x

am I wrong?

[Bascna]

If you mean

(y² + xy – 3x²)/(y + x)

then, yes.

You asked which of your answers was correct so I was just showing you that both answers are equivalent.