. 9/11-x+11/x-9=2

To solve the equation \( \frac{9}{11-x} + \frac{11}{x-9} = 2 \), we can first find a common denominator for the two fractions on the left side:

\( \frac{9(x-9)}{(11-x)(x-9)} + \frac{11(11-x)}{(11-x)(x-9)} = 2 \)

Now, we can combine the fractions:

\( \frac{9(x-9) + 11(11-x)}{(11-x)(x-9)} = 2 \)

Expand both the numerator and denominator:

\( \frac{9x - 81 + 121 - 11x}{(11-x)(x-9)} = 2 \)

Combine like terms in the numerator:

\( \frac{-2x + 40}{(11-x)(x-9)} = 2 \)

Now, set the equation equal to zero by moving the 2 to the left side:

\( \frac{-2x + 40}{(11-x)(x-9)} - 2 = 0 \)

Now, let's simplify the equation further to solve for x.