a\omega + b = \omega + 3\omega^2 + 1 \quad \ ext{(1)}

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$$ 9(x^2 - 4x) - 4(y^2 - 4y) = 44 \frac{1}{n(n+2)} = \frac{A}{n} + \frac{B}{n+2} $$
Factor out leading coefficients:
\boxed{-2x - 2} $$
Factor out leading coefficients:
\boxed{-2x - 2} $$
$$ Find common denominator for $ \frac{1}{51} + \frac{1}{52} $:

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\frac{(x - 2)^2}{\frac{60}{9}} - \frac{(y - 2)^2}{\frac{60}{4}} = 1 Distribute and simplify:
9[(x - 2)^2 - 4] - 4[(y - 2)^2 - 4] = 44 $$ $$ $$

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\frac{(x - 2)^2}{\frac{60}{9}} - \frac{(y - 2)^2}{\frac{60}{4}} = 1 Distribute and simplify:
9[(x - 2)^2 - 4] - 4[(y - 2)^2 - 4] = 44 $$ $$ $$ $$
$$
e 1 $, and $ \omega^2 + \omega + 1 = 0 $.
f(3) = 3^2 - 3(3) + m = 9 - 9 + m = m \frac{1}{2} \left( \left( \frac{1}{1} - \frac{1}{3} \right) + \left( \frac{1}{2} - \frac{1}{4} \right) + \left( \frac{1}{3} - \frac{1}{5} \right) + \cdots + \left( \frac{1}{50} - \frac{1}{52} \right) \right) - Third: $ -x - y = 4 $, from $ (-4, 0) $ to $ (0, -4) $.
$$ a(\omega - \omega^2) = (\omega - \omega^2) + 3(\omega^2 - \omega) $$

$$ $$ $$ $$
$$
e 1 $, and $ \omega^2 + \omega + 1 = 0 $.
f(3) = 3^2 - 3(3) + m = 9 - 9 + m = m \frac{1}{2} \left( \left( \frac{1}{1} - \frac{1}{3} \right) + \left( \frac{1}{2} - \frac{1}{4} \right) + \left( \frac{1}{3} - \frac{1}{5} \right) + \cdots + \left( \frac{1}{50} - \frac{1}{52} \right) \right) - Third: $ -x - y = 4 $, from $ (-4, 0) $ to $ (0, -4) $.
$$ a(\omega - \omega^2) = (\omega - \omega^2) + 3(\omega^2 - \omega) $$

$$ Now solve the system:
$$ Add the two expressions:
\boxed{\frac{21}{2}} $$ $$
Complete the square:
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$$
e 1 $, and $ \omega^2 + \omega + 1 = 0 $.
f(3) = 3^2 - 3(3) + m = 9 - 9 + m = m \frac{1}{2} \left( \left( \frac{1}{1} - \frac{1}{3} \right) + \left( \frac{1}{2} - \frac{1}{4} \right) + \left( \frac{1}{3} - \frac{1}{5} \right) + \cdots + \left( \frac{1}{50} - \frac{1}{52} \right) \right) - Third: $ -x - y = 4 $, from $ (-4, 0) $ to $ (0, -4) $.
$$ a(\omega - \omega^2) = (\omega - \omega^2) + 3(\omega^2 - \omega) $$

$$ Now solve the system:
$$ Add the two expressions:
\boxed{\frac{21}{2}} $$ $$
Complete the square:
Now compute the sum:
$$ So:
This is a hyperbola centered at $ (2, 2) $.
\boxed{(2, 2)} $$
$$
\frac{1}{2} \left( \frac{3}{2} - \frac{103}{2652} \right) = \frac{1}{2} \left( \frac{3978 - 103}{2652} \right) = \frac{1}{2} \cdot \frac{3875}{2652} = \frac{3875}{5304} $$ $$ a(\omega - \omega^2) = (\omega - \omega^2) + 3(\omega^2 - \omega) $$

$$ Now solve the system:
$$ Add the two expressions:
\boxed{\frac{21}{2}} $$ $$
Complete the square:
Now compute the sum:
$$ So:
This is a hyperbola centered at $ (2, 2) $.
\boxed{(2, 2)} $$
$$
\frac{1}{2} \left( \frac{3}{2} - \frac{103}{2652} \right) = \frac{1}{2} \left( \frac{3978 - 103}{2652} \right) = \frac{1}{2} \cdot \frac{3875}{2652} = \frac{3875}{5304} $$ $$ $$
\boxed{2x^4 - 4x^2 + 3} f(\omega) = \omega^4 + 3\omega^2 + 1 = \omega + 3\omega^2 + 1 = a\omega + b $$ $$ \boxed{\frac{3875}{5304}} $$ Solving gives $ A = \frac{1}{2}, B = -\frac{1}{2} $, so:
$$