Question

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Answer 1

((t² - 5t + 25)/(25t² - 1) · (5t² + t)/(t³ + 125) - (t + 5)/(5t² - t)) ÷ 3/(t² + 5t) - (25t + 22)/
/(4 - 20t) =
1) ((t² - 5t + 25)/(25t² - 1) · (5t² + t)/(t³ + 125) = (t² - 5t + 25)/(5t - 1)(5t + 1) · t(5t + 1)/
/(t + 5)(t² - 5t + 25) = t(5t + 1)(t² - 5t + 25)/(5t - 1)(5t + 1)(t² - 5t + 25) = t/(5t - 1)
2) t/(5t - 1) - (t + 5)/(5t² - t) = t/(5t - 1) - (t + 5)/t(5t - 1) = t · t/(5t - 1) · t - (t + 5)/t(5t - 1) =
= t²/t(5t - 1) - (t + 5)/t(5t - 1) = t² - (t + 5)/t(5t - 1) = (t² - t + 5)/t(5t - 1)
3) (t² - t + 5)/t(5t - 1) ÷ 3/(t² + 5t) = (t² - t + 5)/t(5t - 1) ÷ 3/t(t + 5) = (t² - t + 5)/t(5t - 1)· t(t + 5)/3 = t(t + 5)(t² - t + 5)/3 · t(5t - 1)
4) t(t + 5)(t² - t + 5)/3 · t(5t - 1) - (25t + 22)/(4 - 20t) = t(t + 5)(t² - t + 5)/3 · t(5t - 1) - (25t + 22)/(-4)((-1) + 5t) = t(t + 5)(t² - t + 5)/3t(5t - 1) - (25t + 22)/(-4)(5t - 1) = (-4 · t)(t + 5)(t² - t + 5)/(-4) · 3t · (5t -1) - 3t(25t + 22)/3t · (-4)(5t - 1) = ((-4)t² - 20t)(t² - t + 5) - (75t² + 66t)/3t · (-4)(5t - 1) = ((-4t⁴) + 4t³ - 20t² - 20t³ + 20t² - 100t - 75t² - 66t)/3t · (-4)(5t - 1) = ((-4t⁴ - 16t³ + 75t² - 166t)/3t · (-4)(5t - 1) = (-4)(t⁴ + 4t³ - 18,75t² + 41,5t)/3t · (-4)(5t - 1) = (t⁴ + 4t³ - 18,75t² + 41,5t)/3t(5t - 1) = t(t³ + 4t² - 18,75t + 41,5)/3t(5t - 1) =
= (t³ + 4t² - 18,75t + 41,5)/3(5t - 1)