x + 24(1/x) = 11
Solve for x: Answer: x = 8 or x = 3
Solve for x over the real numbers:
x + 24/x = 11
Bring x + 24/x together using the common denominator x:
(x^2 + 24)/x = 11
Multiply both sides by x:
x^2 + 24 = 11 x
Subtract 11 x from both sides:
x^2 - 11 x + 24 = 0
The left hand side factors into a product with two terms:
(x - 8) (x - 3) = 0
Split into two equations:
x - 8 = 0 or x - 3 = 0
Add 8 to both sides:
x = 8 or x - 3 = 0
Add 3 to both sides:
Answer: x = 8 or x = 3