1)Simplify;
2x^2-y^2+xy/x^2-y^2
This step is wrong.
2x^2 - y^2 + xy = xy(2x - y)
There is no common factor of xy.
Instead,
(2x^2-y^2+xy)/(x^2-y^2) = (2x+y)(x-y) / (x+y)(x-y) = (2x+y)/(x+y)
Apologies for the mistake in the previous step.
The correct simplification is:
(2x^2 - y^2 + xy)/(x^2 - y^2) = (2x + y)/(x + y)
To simplify the expression 2x^2 - y^2 + (xy / (x^2 - y^2)), we can start by factoring the numerator and denominator of the fraction separately.
Numerator: 2x^2 - y^2
This expression is a difference of squares, so we can simplify it as follows:
2x^2 - y^2 = (x√2 - y)(x√2 + y)
Denominator: x^2 - y^2
This expression is also a difference of squares, which can be factored as follows:
x^2 - y^2 = (x - y)(x + y)
Now, we can substitute the factored forms of the numerator and denominator back into the original expression:
(2x^2 - y^2) + (xy / (x^2 - y^2)) = (x√2 - y)(x√2 + y) + xy / (x - y)(x + y)
The expression is now completely factored. If you were looking to simplify it further, please let me know.
To simplify the expression, we can first factor the numerator and denominator separately.
For the numerator, we observe that there is a common factor of xy:
2x^2 - y^2 + xy = xy(2x - y)
For the denominator, we can apply the difference of squares formula:
x^2 - y^2 = (x - y)(x + y)
Now, we can simplify the expression:
(2x^2 - y^2 + xy)/(x^2 - y^2) = (xy(2x - y))/((x - y)(x + y))
The final simplified expression is: (xy(2x - y))/((x - y)(x + y))