Solve for X: Finding the Value in 9/x = 3/(x+2)

To solve the equation $\frac{9}{x} = \frac{3}{x+2}$, we'll follow these steps:

• Step 1: Use cross-multiplication to eliminate the fractions.

• Step 2: Simplify the resulting linear equation.

• Step 3: Solve for $x$.

Now, let's work through each step:

Step 1: Cross-multiply to clear the fractions:

$\frac{9}{x} = \frac{3}{x+2}$

Cross-multiplying gives:

$9(x + 2) = 3x$

Step 2: Distribute the 9 on the left side:

$9x + 18 = 3x$

Step 3: Isolate the variable $x$:

Subtract $3x$ from both sides:

$9x + 18 - 3x = 3x - 3x$

This simplifies to:

$6x + 18 = 0$

Subtract 18 from both sides:

$6x = -18$

Divide by 6 to solve for $x$:

$x = \frac{-18}{6}$

Therefore, $x = -3$.

The solution to the problem is $x = -3$.