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

Math
z2-1z-2z+1
Simplify the numerator.
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Rewrite 1 as 12.
z2-12z-2z+1
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=z and b=1.
(z+1)(z-1)z-2z+1
(z+1)(z-1)z-2z+1
Simplify terms.
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Subtract 2z from z.
(z+1)(z-1)-z+1
Simplify terms.
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Cancel the common factor of z-1 and -z+1.
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Factor -1 out of z.
(z+1)(-1(-z)-1)-z+1
Rewrite -1 as -1(1).
(z+1)(-1(-z)-1(1))-z+1
Factor -1 out of -1(-z)-1(1).
(z+1)(-1(-z+1))-z+1
Cancel the common factor.
(z+1)⋅-1(-z+1)-z+1
Divide (z+1)⋅-1 by 1.
(z+1)⋅-1
(z+1)⋅-1
Apply the distributive property.
z⋅-1+1⋅-1
Simplify the expression.
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Move -1 to the left of z.
-1⋅z+1⋅-1
Multiply -1 by 1.
-1⋅z-1
-1⋅z-1
-1⋅z-1
Rewrite -1z as -z.
-z-1
-z-1
Simplify (z^2-1)/(z-2z+1)

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