(((t² - 5t + 25)/(25t² - 1)) · ((5t² + t)/(t³ + 125)) - ((t + 5)/(5t² - t))) ÷ (4/(t² + 5t)) - ((25t + +22)/(4 - 20t)) = (t + 173,7)/(2t +21,6)
1) (((t² - 5t + 25)/(25t² - 1)) · ((5t² + t)/(t³ + 125)) = ((t - 5)²/(5t - 1)(5t + 1)) · (t(5t + 1)/(t + +5) · (t² - 5t + 25)) = ((t - 5)(t - 5)/(5t - 1)(5t + 1)) · (t(5t + 1)/(t + 5)(t² - 5t + 25)) = (t - 5)(t - 5)t(5t + 1)/(5t - 1)(5t + 1)(t + 5)(t² - 5t + 25) = (t - 5)(t - 5)t/(5t - 1)(t + 5)(t² - 5t + 25)
2) ((t - 5)(t - 5)t/(5t - 1)(t + 5)(t² - 5t + 25)) - ((t + 5)/(5t² - t)) = ((t - 5)(t - 5)t/(5t - 1)(t + 5)(t² - 5t + 25)) - ((t + 5)/t(5t - 1)) = ((t - 5)(t - 5)t · t/(5t - 1)(t + 5)(t² - 5t + 25) ·t) - ((t + 5) ·
(t + 5)(t² - 5t + 25))/(t + 5)(t² - 5t + 25)(5t - 1) · t = ((t - 5)(t - 5)t · t) - ((t + 5)(t + 5)(t² - 5t + 25))/(t + 5)(t² - 5t + 25)(5t - 1) · t = (t²(t - 5)² - ((t+5)(t³- 125))/(t + 5)(t² - 5t + 25)(5t - -1)t = (t²(t² - 10 · t + 25) - (t⁴ + 5t³ - 125t - 625))/(t + 5)(t² - 5t + 25)(5t - 1)t = (t⁴ - 10t³ + + 25t² - t⁴ - 5t³ + 125t + 625)/(t + 5)(t² - 5t + 25)(5t - 1)t = (t⁴ - t⁴ - 10t³ - 5t³ + 25t² + +125t + 625)/(t + 5)(t² - 5t + 25)(5t - 1)t = ((-15t³ + 25t² + 125t + 625)/(t + 5)(t² - 5t + + 25)(5t - 1)t
3) ((-15t³ + 25t² + 125t + 625)/(t + 5)(t² - 5t + 25)(5t - 1)t) ÷ (4/(t² + 5t)) = ((-15t³ + 25t² + 125t + 625)/(t + 5)(t² - 5t + 25)(5t - 1)t) · ((t² + 5t)/4) = ((-15t³ + 25t²+ 125t + 625)/(t+ + 5)(t² - 5t + 25)(5t - 1)t) · (t(t + 5)/4) = ((-15t³ + 25t²+ 125t + 625)/(t² - 5t + 25)(5t - 1) · · 4 = ((-1)(15t³ - 25t²- 125t - 625)/(t² - 5t + 25)(20t - 4) = ((-1)(15t³ - 25t²- 125t - 625)/ /(t² - 5t + 25)(-1)(-20t + 4) = (15t³ - 25t²- 125t - 625)/(t² - 5t + 25)(4 -20t)
4) ((15t³ - 25t² - 125t - 625)/(t² - 5t + 25)(4 - 20t)) - ((25t + 22)/(4 - 20t)) = ((15t³ -
-25t² - 125t - 625)/(t² - 5t + 25)(4 - 20t)) - ((t² - 5t + 25)(25t + 22)/(4 - 20t)(t² - 5t + 25)) = ((15t³ - 25t² - 125t - 625) - (t² - 5t + 25)(25t + 22))/((t² - 5t + 25)(4 - 20t)) = (15t³ - 25t² - 125t - 625 - (25t³ - 125t² + 625t + 22t² - 110t + 550))/((t² - 5t + 25)(4 - 20t)) = (15t³ - 25t² - 125t - 625 - 25t³ + 125t² - 625t - 22t² + 110t - 550)/((t² - 5t + 25)(4 - 20t)) = (15t³ - 25t³ - 25t² + 125t² - 22t² - 125t - 625t + 110 - 625 - 550)/((t² - 5t + 25)(4 - 20t)) = ((-10t³) + 100t² - 22t² - 750t + 110t - 1175))/((t² - 5t + 25)(4 - 20t))= = ((-10t³) + 78t² - 640t - 1175)/( 4t² - 20t + 100 - 20t³ + 100t² - 400t) = ((-10t³) + 78t²- - 640t - 1175)/((-20t³) + 4t² + 100t² - 20t - 400t + 100) = ((-10t³) + 78t² - 640t - 1175)/ /((-20t³) + 104t² - 420t + 100) = 2((-5t³) + 39t² - 320t - 587,5)/2((-10t³) + 52t² - 210t + 50) = ((-5t³) + 39t² - 320t - 587,5)/((-10t³) + 52t² - 210t + 50) = (-1) · 5(t³ - 7,8t² + 64t + 117,5)/5 · (-1)(2t³ - 10,4t² +42 t-10) = (t³ - 7,8t² + 64t + 117,5)/(2t³ - 10,4t² + 42t - - 10) = t((t² - 7,8t + 64) + 117,5)/t((2t² - 10,4t + 42) - 10) = ((t² - 7,8t) + 64 + 117,5)/((2t² - 10,4t) + 42 - 10) = t((t - 7,8) + 64 + 117,5)/t((2t - 10,4) +42 - 10) = (t - 7,8 + 64 + 117,5) /(2t - 10,4 + 42 - 10) = (t + 56,2 + 117,5)/(2t + 31,6 - 10) = (t + 173,7)/(2t +21,6)