General simplification
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$$- y^{4} + 9 y^{2} - 13$$
/ ____________\ / ____________\ / ____________\ / ____________\
| / ____ | | / ____ | | / ____ | | / ____ |
| / 9 \/ 29 | | / 9 \/ 29 | | / 9 \/ 29 | | / 9 \/ 29 |
|x + / - - ------ |*|x - / - - ------ |*|x + / - + ------ |*|x - / - + ------ |
\ \/ 2 2 / \ \/ 2 2 / \ \/ 2 2 / \ \/ 2 2 /
$$\left(x - \sqrt{\frac{9}{2} - \frac{\sqrt{29}}{2}}\right) \left(x + \sqrt{\frac{9}{2} - \frac{\sqrt{29}}{2}}\right) \left(x + \sqrt{\frac{\sqrt{29}}{2} + \frac{9}{2}}\right) \left(x - \sqrt{\frac{\sqrt{29}}{2} + \frac{9}{2}}\right)$$
(((x + sqrt(9/2 - sqrt(29)/2))*(x - sqrt(9/2 - sqrt(29)/2)))*(x + sqrt(9/2 + sqrt(29)/2)))*(x - sqrt(9/2 + sqrt(29)/2))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} + 9 y^{2}\right) - 13$$
To do this, let's use the formula
$$a y^{4} + b y^{2} + c = a \left(m + y^{2}\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -1$$
$$b = 9$$
$$c = -13$$
Then
$$m = - \frac{9}{2}$$
$$n = \frac{29}{4}$$
So,
$$\frac{29}{4} - \left(y^{2} - \frac{9}{2}\right)^{2}$$
$$- y^{4} + 9 y^{2} - 13$$
Assemble expression
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$$- y^{4} + 9 y^{2} - 13$$
Rational denominator
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$$- y^{4} + 9 y^{2} - 13$$
$$- y^{4} + 9 y^{2} - 13$$
$$- y^{4} + 9 y^{2} - 13$$
Combining rational expressions
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$$y^{2} \left(9 - y^{2}\right) - 13$$
$$- y^{4} + 9 y^{2} - 13$$