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

Math
(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+xy.
Tap for more steps…
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
Write each expression with a common denominator of (x-y)(x+y), by multiplying each by an appropriate factor of 1.
Tap for more steps…
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
Simplify the numerator.
Tap for more steps…
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.
Tap for more steps…
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.
Tap for more steps…
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
Simplify terms.
Tap for more steps…
Cancel the common factor of x2+y2.
Tap for more steps…
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.
Tap for more steps…
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))

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top