https://file.aiquickdraw.com/mathbot/file/172584186985316zr2vla.jpg

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.

Solve the equation: 3/(x+9) - 2/(x+5) = 0

Learn how to solve the rational equation 3/(x+9) - 2/(x+5) = 0 step-by-step. This problem covers key algebraic concepts such as combining fractions with different denominators and solving rational equations by setting the numerator equal to zero. Suitable for students in Grades 9-10.

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