Solve the Fraction Equation: 9/(x+5) = 11/(2-x)

To solve this problem, follow these steps:

• Step 1: Cross-multiply to eliminate the fractions.
• Step 2: Solve the resulting linear equation.

Let's proceed step-by-step:

Step 1: Given the equation $\frac{9}{x+5} = \frac{11}{2-x}$, we will cross-multiply:

$9 \times (2 - x) = 11 \times (x + 5)$

Simplify both sides:

$18 - 9x = 11x + 55$

Step 2: Solve for $x$.

First, rearrange the terms to get all terms involving $x$ on one side:

$18 - 55 = 11x + 9x$

$-37 = 20x$

Divide both sides by 20 to solve for $x$:

$x = -\frac{37}{20}$

Thus, the solution to the problem is $x = -\frac{37}{20}$.