Verified answer

1/(√X+2) + 1/(√X-3) = 5/6

√X-2)/(√X+2)*(√X-2) + (√X+3)/(√X-3)*(√X+3) = 5/6

(√X-2)/(x-4) + (√X+3)/(x-9) = 5/6

(x-9)(√X-2)/(x-4)(x-9) + (x-4)(√X+3)/(x-9)(x-4) = 5/6

vamos lá

1/a + 1/b = (a + b)/ab

S = a + b = 5

P = a*b = 6

x² - Sx + P = 0

x² - 5x + 6 = 0

Δ² = 25 - 4*1*6 = 25 - 24 = 1

x' = (5 + 1)/2 = 3

x" = (5 - 1)/2 = 2

a = 3

b = 2

(2 + 3)/6 = 2/6 + 3/6 = 1/3 + 1/2

1/√(x+2) = 1/3

1/(x + 2) = 1/9

x + 2 = 9

x = 7

1/√(x - 3) = 1/2

1/(x - 3) = 1/4

x - 3 = 4

x = 7

verificação

1/√(x+ 2) + 1/√(x - 3)

1/√(7+ 2) + 1/√(7 - 3)

1/√9 + 1/√4

1/3 + 1/2 = 5/6