# Simplify (z-(z/(z-((z^2)/(z+1)))))/(z/z)

z-(zz-(z2z+1))zz
Reduce the expression by cancelling the common factors.
Cancel the common factor of z.
Cancel the common factor.
z-(zz-(z2z+1))zz
Divide 1 by 1.
z-(zz-(z2z+1))1
z-(zz-(z2z+1))1
Divide z-(zz-(z2z+1)) by 1.
z-(zz-(z2z+1))
z-(zz-(z2z+1))
Simplify each term.
Simplify the denominator.
To write z as a fraction with a common denominator, multiply by z+1z+1.
z-zz(z+1)z+1-z2z+1
Combine the numerators over the common denominator.
z-zz(z+1)-z2z+1
Reorder terms.
z-z-z2+z(z+1)z+1
Rewrite -z2+z(z+1)z+1 in a factored form.
Factor z out of -z2+z(z+1).
Factor z out of -z2.
z-zz(-z)+z(z+1)z+1
Factor z out of z(-z)+z(z+1).
z-zz(-z+z+1)z+1
z-zz(-z+z+1)z+1
z-zz(0+1)z+1
z-zz⋅1z+1
z-zz⋅1z+1
Multiply z by 1.
z-zzz+1
z-zzz+1
Multiply the numerator by the reciprocal of the denominator.
z-(zz+1z)
Cancel the common factor of z.
Cancel the common factor.
z-(zz+1z)
Rewrite the expression.
z-(z+1)
z-(z+1)
Apply the distributive property.
z-z-1⋅1
Multiply -1 by 1.
z-z-1
z-z-1