To solve the equation:
1/(x+1) + 9/(x+9) = 1
First, we can simplify the equation by finding a common denominator:
((x+9)+9(x+1))/(x+1)(x+9) = 1
Simplifying the numerator, we get:
(10x+18)/(x+1)(x+9) = 1
Cross-multiplying gives:
10x+18 = (x+1)(x+9)
Expanding the right side of the equation, we get:
10x+18 = x^2+10x+9
Simplifying and rearranging gives:
x^2-9 = 0
Using the quadratic formula, we solve for x:
x = (±sqrt(81))/1
x = ±9
Therefore, the solutions to the equation are x = -9 and x = 9.