Solve Complex Fraction Expression: [(25+3·2)-6]:5 ÷ (4+1) - 76/19

Let's solve the given expression step-by-step, applying the order of operations, commonly known by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
The given expression is:
$\frac{[(25+3\cdot2)-6]:5}{4+1}-\frac{76}{19}$

Step 1: Solve inside the innermost parentheses
We start by solving the expression inside the square brackets $[\cdot]$:

• Simplify: $3\cdot2 = 6$
• Add: $25 + 6 = 31$
• Subtract: $31 - 6 = 25$

Thus, $[ (25 + 3 \cdot 2) - 6 ] = 25$.

Step 2: Solve the division inside the fraction
Next, we calculate:

• Divide: $25:5 = 5$

Thus, the fraction becomes: $\frac{5}{4+1}$

Step 3: Solve the denominator of the fraction

• Add: $4 + 1 = 5$

Now the entire fraction simplifies to: $\frac{5}{5} = 1$.

Step 4: Solve the subtraction
Finally, perform the subtraction:

• Subtract: $1 - \frac{76}{19}$

Since $76 \div 19 = 4$, then:

• Subtract: $1 - 4 = -3$

Thus, the solution is $-3$.

The solution to the question is: -3