Odpowiedź:
a)
(2x+7)/(x-1)=x+1 / * (x - 1)
2x + 7 = (x + 1) * (x - 1)
2x + 7 = x² - x + x - 1
2x + 7 = x² - 1
x² - 1 - 2x - 7 = 0
x² - 2x - 8 = 0
Δ = b² - 4ac
Δ = ( - 2)² - 4*1*( - 8) = 4 + 32 = 36
√Δ = 6
x1 = ( - b - √Δ)/2a = (2 - 6)/2*1 = -4/2 = -2
x2 = ( - b + √Δ)/2a = (2 + 6)/2*1 = 8/2 = 4
x1 = - 2
x2 = 4
b)
(x+3)/(x-1)=6/(x-3) /* (x - 1) * (x - 3)
(x + 3 ) * (x - 3 ) = 6 * (x - 1)
x² - 3x + 3x - 9 = 6x - 6
x² - 9 = 6x - 6
x² - 6x - 9 + 6 = 0
x² - 6x - 3 = 0
Δ = ( - 6)² - 4*1*( - 3) = 36 + 12 = 48
√Δ = 4√3
x1 = (6 - 4√3)/2 = 3 - 2√3
x2 = (6 + 4√3)/2 = 3 + 2√3
x1 = 3 - 2√3
x2 = 3 + 2√3
Szczegółowe wyjaśnienie:
