The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{2} + y\right) - 2$$
To do this, let's use the formula
$$a y^{2} + b y + c = a \left(m + y\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -1$$
$$b = 1$$
$$c = -2$$
Then
$$m = - \frac{1}{2}$$
$$n = - \frac{7}{4}$$
So,
$$- \left(y - \frac{1}{2}\right)^{2} - \frac{7}{4}$$
/ ___\ / ___\
| 1 I*\/ 7 | | 1 I*\/ 7 |
|x + - - + -------|*|x + - - - -------|
\ 2 2 / \ 2 2 /
$$\left(x + \left(- \frac{1}{2} - \frac{\sqrt{7} i}{2}\right)\right) \left(x + \left(- \frac{1}{2} + \frac{\sqrt{7} i}{2}\right)\right)$$
(x - 1/2 + i*sqrt(7)/2)*(x - 1/2 - i*sqrt(7)/2)
General simplification
[src]
$$- y^{2} + y - 2$$
Combining rational expressions
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$$y \left(1 - y\right) - 2$$
Assemble expression
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$$- y^{2} + y - 2$$
Rational denominator
[src]
$$- y^{2} + y - 2$$