What is (z^2-z+0.64)/((z-1)(z-0.36))-1 ?

The solution to (z^2-z+0.64)/((z-1)(z-0.36))-1 is (0.36z+0.28)/((z-1)(z-0.36))

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simplify (z^2-z+0.64)/((z-1)(z-0.36))-1

simplify

\frac{z ^{2} - z + 0.64}{( z - 1 ) ( z - 0.36 )} - 1

\frac{0.36 z + 0.28}{( z - 1 ) ( z - 0.36 )}

Solution steps

\frac{z ^{2} - z + 0.64}{( z - 1 ) ( z - 0.36 )} - 1

Apply the fraction rule:

a + \frac{b}{c} = \frac{a c + b}{c}

= \frac{- 1 \cdot ( z - 1 ) ( z - 0.36 ) + z ^{2} - z + 0.64}{( z - 1 ) ( z - 0.36 )}

Apply rule:

1 \cdot a = a

- 1 \cdot (z - 1) (z - 0.36) = - (z - 1) (z - 0.36)

= \frac{- ( z - 1 ) ( z - 0.36 ) + z ^{2} - z + 0.64}{( z - 1 ) ( z - 0.36 )}

Simplify

- (z - 1) (z - 0.36) + z^{2} - z + 0.64 : 0.36 z + 0.28

= \frac{0.36 z + 0.28}{( z - 1 ) ( z - 0.36 )}

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What is (z^2-z+0.64)/((z-1)(z-0.36))-1 ?
The solution to (z^2-z+0.64)/((z-1)(z-0.36))-1 is (0.36z+0.28)/((z-1)(z-0.36))