2*(543/1000+k^2)*(713/1000+k^2-2*k+1)*1/((2493/500+k^2)*(k+1)^2) если k=-1/3 (упростите выражение)

$$frac{2 left(k^{2} + frac{543}{1000}right)}{left(k + 1right)^{2} left(k^{2} + frac{2493}{500}right)} left(- 2 k + k^{2} + frac{713}{1000} + 1right)$$

$$frac{2 left(k^{2} + frac{543}{1000}right)}{left(k + 1right)^{2} left(k^{2} + frac{2493}{500}right)} left(- 2 k + k^{2} + frac{713}{1000} + 1right)$$

((2*(543/1000 + (-1/3)^2))*(713/1000 + (-1/3)^2 – 2*(-1/3) + 1))/((2493/500 + (-1/3)^2)*((-1/3) + 1)^2)

$$frac{2 left((-1/3)^{2} + frac{543}{1000}right)}{left((-1/3) + 1right)^{2} left((-1/3)^{2} + frac{2493}{500}right)} left(- 2 (-1/3) + (-1/3)^{2} + frac{713}{1000} + 1right)$$

((2*(543/1000 + (-1/3)^2))*(713/1000 + (-1/3)^2 – 2*(-1)/3 + 1))/((2493/500 + (-1/3)^2)*(-1/3 + 1)^2)

$$frac{left(1 + – frac{-2}{3} + left(- frac{1}{3}right)^{2} + frac{713}{1000}right) 2 left(left(- frac{1}{3}right)^{2} + frac{543}{1000}right)}{left(- frac{1}{3} + 1right)^{2} left(left(- frac{1}{3}right)^{2} + frac{2493}{500}right)}$$

131968879/91748000

$$frac{131968879}{91748000}$$

$$frac{left(2 k^{2} + frac{543}{500}right) left(k^{2} – 2 k + frac{1713}{1000}right)}{left(k + 1right)^{2} left(k^{2} + frac{2493}{500}right)}$$

2.0*(0.543 + k^2)*(1.713 + k^2 – 2.0*k)/((1.0 + k)^2*(4.986 + k^2))

$$frac{left(2000 k^{2} + 1086right) left(1000 k^{2} – 2000 k + 1713right)}{2000 left(k + 1right)^{2} left(500 k^{2} + 2493right)}$$

$$frac{left(1000 k^{2} + 543right) left(1000 k^{2} – 2000 k + 1713right)}{1000 left(k + 1right)^{2} left(500 k^{2} + 2493right)}$$

/ 2 / 2
543 + 1000*k /*1713 – 2000*k + 1000*k /
—————————————–
2 / 2
1000*(1 + k) *2493 + 500*k /

$$frac{left(1000 k^{2} + 543right) left(1000 k^{2} – 2000 k + 1713right)}{1000 left(k + 1right)^{2} left(500 k^{2} + 2493right)}$$

$$frac{left(2 k^{2} + frac{543}{500}right) left(k^{2} – 2 k + frac{1713}{1000}right)}{left(k + 1right)^{2} left(k^{2} + frac{2493}{500}right)}$$

2 3
4055841 + 3730000*k + 4000000*k + 11058000*k
2 – ———————————————————
4 3 2
2493000 + 500000*k + 1000000*k + 2993000*k + 4986000*k

$$- frac{4000000 k^{3} + 3730000 k^{2} + 11058000 k + 4055841}{500000 k^{4} + 1000000 k^{3} + 2993000 k^{2} + 4986000 k + 2493000} + 2$$

/ 2 / 2
543 + 1000*k /*1713 – 2000*k + 1000*k /
—————————————–
2 / 2
1000*(1 + k) *2493 + 500*k /

$$frac{left(1000 k^{2} + 543right) left(1000 k^{2} – 2000 k + 1713right)}{1000 left(k + 1right)^{2} left(500 k^{2} + 2493right)}$$

/543 2 /713 2
2*|—- + k |*|—- + k – 2*k + 1|
1000 / 1000 /
———————————–
/2493 2 2
|—- + k |*(k + 1)
500 /

$$frac{2}{left(k + 1right)^{2} left(k^{2} + frac{2493}{500}right)} left(k^{2} + frac{543}{1000}right) left(- 2 k + k^{2} + frac{713}{1000} + 1right)$$