9b^2 - 8a 
/
12ab

= 
Xb
/
Ya
-
2
/
Zb

X= 3
Y= ?
Z= ?

To solve the equation:

\[
\frac{9b^2 - 8a}{12ab} = \frac{Xb}{Ya} - \frac{2}{Zb}
\]

where \(X = 3\), we can follow these steps:

### Step 1: Split the expression on the right-hand side.
Given:
\[
\frac{Xb}{Ya} - \frac{2}{Zb}
\]
Substitute \(X = 3\):
\[
\frac{3b}{Ya} - \frac{2}{Zb}
\]

### Step 2: Simplify the left-hand side.
We need to split the left-hand side into two parts, just like the right-hand side:
\[
\frac{9b^2 - 8a}{12ab} = \frac{9b^2}{12ab} - \frac{8a}{12ab}
\]

Simplify each term:
- \(\frac{9b^2}{12ab} = \frac{3b}{4a}\)
- \(\frac{8a}{12ab} = \frac{2}{3b}\)

So:
\[
\frac{9b^2 - 8a}{12ab} = \frac{3b}{4a} - \frac{2}{3b}
\]

### Step 3: Compare both sides.
Now we compare:
\[
\frac{3b}{4a} - \frac{2}{3b} = \frac{3b}{Ya} - \frac{2}{Zb}
\]

From this, we can directly match:
- \(\frac{3b}{4a} = \frac{3b}{Ya} \Rightarrow Y = 4\)
- \(\frac{2}{3b} = \frac{2}{Zb} \Rightarrow Z = 3\)

### Final values:
- \(Y = 4\)
- \(Z = 3\)

Would you like more details on any step?

Here are five related questions for further practice:
1. What happens if \(X\) is a different value?
2. How do you simplify expressions with multiple variables?
3. How would the solution change if \(Z = 4\)?
4. Can you apply the same steps to a different equation?
5. How do you verify the solution?

**Tip:** Always try to simplify both sides of the equation before matching terms.

9b^2 - 8a / 12ab = Xb / Ya - 2 / Zb; X = 3, Y = ?, Z = ?

This tutorial walks you through solving the equation (9b^2 - 8a) / (12ab) = (Xb) / (Ya) - 2 / (Zb) given X = 3. We simplify both sides, compare terms, and find the values of Y and Z. Core algebra concepts, such as simplifying rational expressions and equation balancing, are covered. Ideal for Grades 9-12 students.

Math Problem Statement

= Xb / Ya

Solution

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