The equation in the image is:

$\frac{3}{x+9} - \frac{2}{x+5} = 0$

Let's solve this step by step.

Step 1: Combine the two fractions

To combine the two fractions, we need a common denominator. The common denominator between $x + 9$ and $x + 5$ is their product, $(x + 9)(x + 5)$. Rewrite the equation with this common denominator:

$\frac{3(x+5) - 2(x+9)}{(x+9)(x+5)} = 0$

Step 2: Simplify the numerator

Expand both terms in the numerator:

$3(x+5) = 3x + 15$ $2(x+9) = 2x + 18$

Now substitute these into the equation:

$\frac{(3x + 15) - (2x + 18)}{(x+9)(x+5)} = 0$

Step 3: Simplify further

Simplify the numerator by distributing the negative sign and combining like terms:

$(3x + 15) - (2x + 18) = 3x + 15 - 2x - 18 = x - 3$

So the equation becomes:

$\frac{x - 3}{(x+9)(x+5)} = 0$

Step 4: Solve for $x$

For this fraction to be zero, the numerator must be zero:

$x - 3 = 0$

Solving this:

$x = 3$

Step 5: Check for restrictions

The values $x = -9$ and $x = -5$ would make the denominators zero, which are not allowed. Since $x = 3$ does not violate these restrictions, it is a valid solution.

Final Answer:

$x = 3$

Would you like more details on any part of the solution?

Here are 5 related questions you could explore:

1. How do you solve rational equations with more than two fractions?
2. What happens if a fraction’s denominator equals zero in an equation?
3. How can you verify a solution for a rational equation?
4. What are extraneous solutions in rational equations, and how do they occur?
5. How do you find the least common denominator in complex rational equations?

Tip: Always check for restrictions by setting the denominators not equal to zero before concluding the solution of rational equations.