# Combine (7zy)/(z^2-y^2)+(3z-y)/(z+y)

7zyz2-y2+3z-yz+y
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=z and b=y.
7zy(z+y)(z-y)+3z-yz+y
To write 3z-yz+y as a fraction with a common denominator, multiply by z-yz-y.
7zy(z+y)(z-y)+3z-yz+y⋅z-yz-y
Simplify terms.
Multiply 3z-yz+y and z-yz-y.
7zy(z+y)(z-y)+(3z-y)(z-y)(z+y)(z-y)
Combine the numerators over the common denominator.
7zy+(3z-y)(z-y)(z+y)(z-y)
7zy+(3z-y)(z-y)(z+y)(z-y)
Simplify the numerator.
Expand (3z-y)(z-y) using the FOIL Method.
Apply the distributive property.
7zy+3z(z-y)-y(z-y)(z+y)(z-y)
Apply the distributive property.
7zy+3z⋅z+3z(-y)-y(z-y)(z+y)(z-y)
Apply the distributive property.
7zy+3z⋅z+3z(-y)-yz-y(-y)(z+y)(z-y)
7zy+3z⋅z+3z(-y)-yz-y(-y)(z+y)(z-y)
Simplify and combine like terms.
Simplify each term.
Multiply z by z by adding the exponents.
Move z.
7zy+3(z⋅z)+3z(-y)-yz-y(-y)(z+y)(z-y)
Multiply z by z.
7zy+3z2+3z(-y)-yz-y(-y)(z+y)(z-y)
7zy+3z2+3z(-y)-yz-y(-y)(z+y)(z-y)
Rewrite using the commutative property of multiplication.
7zy+3z2+3⋅-1(zy)-yz-y(-y)(z+y)(z-y)
Multiply 3 by -1.
7zy+3z2-3(zy)-yz-y(-y)(z+y)(z-y)
Multiply y by y.
7zy+3z2-3zy-yz-1⋅-1y2(z+y)(z-y)
Multiply -1 by -1.
7zy+3z2-3zy-yz+1y2(z+y)(z-y)
Multiply y2 by 1.
7zy+3z2-3zy-yz+y2(z+y)(z-y)
7zy+3z2-3zy-yz+y2(z+y)(z-y)
Subtract yz from -3zy.
Move z.
7zy+3z2-3yz-yz+y2(z+y)(z-y)
Subtract yz from -3yz.
7zy+3z2-4yz+y2(z+y)(z-y)
7zy+3z2-4yz+y2(z+y)(z-y)
7zy+3z2-4yz+y2(z+y)(z-y)
Subtract 4yz from 7zy.
Move z.
3z2+7yz-4yz+y2(z+y)(z-y)
Subtract 4yz from 7yz.
3z2+3yz+y2(z+y)(z-y)
3z2+3yz+y2(z+y)(z-y)
3z2+3yz+y2(z+y)(z-y)
Combine (7zy)/(z^2-y^2)+(3z-y)/(z+y)

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