## Simplifying the Expression: (8/9) x (4/5) x (5/6) - (9/5) x (8/9)

This expression involves multiplication and subtraction of fractions. To solve it, we will follow the order of operations (PEMDAS/BODMAS) and simplify step-by-step.

### Step 1: Multiplication

Let's start by performing the multiplications:

**(8/9) x (4/5) x (5/6):**- Multiply the numerators: 8 x 4 x 5 = 160
- Multiply the denominators: 9 x 5 x 6 = 270
- The result: 160/270

**(9/5) x (8/9):**- Multiply the numerators: 9 x 8 = 72
- Multiply the denominators: 5 x 9 = 45
- The result: 72/45

Now, our expression looks like this: **(160/270) - (72/45)**

### Step 2: Simplification (Optional)

Before subtraction, we can simplify both fractions by finding their greatest common factors:

**160/270:**The greatest common factor is 10.- 160 / 10 = 16
- 270 / 10 = 27
- Simplified fraction: 16/27

**72/45:**The greatest common factor is 9.- 72 / 9 = 8
- 45 / 9 = 5
- Simplified fraction: 8/5

The expression now is: **(16/27) - (8/5)**

### Step 3: Subtraction

To subtract fractions, they must have a common denominator. The least common multiple of 27 and 5 is 135.

**(16/27):**Multiply numerator and denominator by 5: (16 * 5) / (27 * 5) = 80/135**(8/5):**Multiply numerator and denominator by 27: (8 * 27) / (5 * 27) = 216/135

Now, the expression is: **(80/135) - (216/135)**

Finally, subtract the numerators and keep the denominator: **(80 - 216) / 135 = -136/135**

### Final Answer

The simplified result of the expression (8/9) x (4/5) x (5/6) - (9/5) x (8/9) is **-136/135**.