Equation

t + 7    t2 - 8t + 16

= - 4 +

2t + 1    t - 4

  The common denominator is (t - 4)(t - 4). Multiple both sides by (t - 4)(t - 4).

(t - 4)(t - 4)

t + 7    (t - 4)(t - 4)

= - 4(t - 4)(t - 4) + (t - 4)(t - 4)

2t + 1    t - 4

t + 7 = -4(t - 4)(t - 4) + (t - 4)(2t + 1)

t + 7 = -4(t² - 8t + 16) + (t - 4)(2t + 1)

t + 7 = -4t² + 32t - 64 + 2t² + t - 8t - 4

t + 7 = -2t² + 25t - 68

2t² - 25t + 68 + t + 7 = 0

2t² - 24t + 75 = 0

t = (12 ± i√6)/2
return