(xx-y-yx+y)÷x2+y2x2+xy

To divide by a fraction, multiply by its reciprocal.

(xx-y-yx+y)x2+xyx2+y2

Factor x out of x2.

(xx-y-yx+y)x⋅x+xyx2+y2

Factor x out of xy.

(xx-y-yx+y)x⋅x+x(y)x2+y2

Factor x out of x⋅x+x(y).

(xx-y-yx+y)x(x+y)x2+y2

(xx-y-yx+y)x(x+y)x2+y2

To write xx-y as a fraction with a common denominator, multiply by x+yx+y.

(xx-y⋅x+yx+y-yx+y)x(x+y)x2+y2

To write -yx+y as a fraction with a common denominator, multiply by x-yx-y.

(xx-y⋅x+yx+y-yx+y⋅x-yx-y)x(x+y)x2+y2

Multiply xx-y and x+yx+y.

(x(x+y)(x-y)(x+y)-yx+y⋅x-yx-y)x(x+y)x2+y2

Multiply yx+y and x-yx-y.

(x(x+y)(x-y)(x+y)-y(x-y)(x+y)(x-y))x(x+y)x2+y2

Reorder the factors of (x-y)(x+y).

(x(x+y)(x+y)(x-y)-y(x-y)(x+y)(x-y))x(x+y)x2+y2

(x(x+y)(x+y)(x-y)-y(x-y)(x+y)(x-y))x(x+y)x2+y2

Combine the numerators over the common denominator.

x(x+y)-y(x-y)(x+y)(x-y)⋅x(x+y)x2+y2

Apply the distributive property.

x⋅x+xy-y(x-y)(x+y)(x-y)⋅x(x+y)x2+y2

Multiply x by x.

x2+xy-y(x-y)(x+y)(x-y)⋅x(x+y)x2+y2

Apply the distributive property.

x2+xy-yx-y(-y)(x+y)(x-y)⋅x(x+y)x2+y2

Multiply y by y.

x2+xy-yx-1⋅-1y2(x+y)(x-y)⋅x(x+y)x2+y2

Simplify each term.

Multiply -1 by -1.

x2+xy-yx+1y2(x+y)(x-y)⋅x(x+y)x2+y2

Multiply y2 by 1.

x2+xy-yx+y2(x+y)(x-y)⋅x(x+y)x2+y2

x2+xy-yx+y2(x+y)(x-y)⋅x(x+y)x2+y2

Subtract yx from xy.

Move y.

x2+xy-xy+y2(x+y)(x-y)⋅x(x+y)x2+y2

Subtract xy from xy.

x2+0+y2(x+y)(x-y)⋅x(x+y)x2+y2

x2+0+y2(x+y)(x-y)⋅x(x+y)x2+y2

Add x2 and 0.

x2+y2(x+y)(x-y)⋅x(x+y)x2+y2

x2+y2(x+y)(x-y)⋅x(x+y)x2+y2

Cancel the common factor of x2+y2.

Cancel the common factor.

x2+y2(x+y)(x-y)⋅x(x+y)x2+y2

Rewrite the expression.

1(x+y)(x-y)(x(x+y))

1(x+y)(x-y)(x(x+y))

Cancel the common factor of x+y.

Factor x+y out of x(x+y).

1(x+y)(x-y)((x+y)x)

Cancel the common factor.

1(x+y)(x-y)((x+y)x)

Rewrite the expression.

1x-yx

1x-yx

Combine 1x-y and x.

xx-y

xx-y

Simplify (x/(x-y)-y/(x+y))÷((x^2+y^2)/(x^2+xy))