Calculate the following, leaving your answer as a fraction (lowest) or in decimal form.

4(2+1)²
--------
3(1)²

I'll be glad to check your answer.

Well first you need to do whats inside the parentheses first because of order of operations.

Lets take the denominator (top half) first.

4(2+1)^2

2=1=3
3^2=9
9x4=36
_______

Now take the second half.
(1)^2= 1
3x1=3

Now since it's in a fraction from 36 over 3, you simply divide the two numbers.
36/3 gives you a final answer of 12.

To solve this expression, you need to follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division - from left to right, Addition and Subtraction - from left to right).

Let's break it down step by step:

Step 1: Simplify inside the parentheses.
Inside the parentheses, we have (2+1), which equals 3. So, the expression becomes:

4(3)²
------
3(1)²

Step 2: Solve the exponents.
The exponent here is ² (squared). To evaluate it, we multiply the number by itself. So, 3² is equal to 3 multiplied by 3, which is 9. The expression now becomes:

4(9)
-----
3(1)²

Step 3: Calculate the multiplications.
Multiply 4 by 9, which gives 36, and multiply 3 by 1, which is 3. The expression is now:

36
---
3

Step 4: Simplify the fraction.
To simplify the fraction, divide the numerator (36) by the denominator (3):

36 ÷ 3 = 12

Therefore, the answer to the expression 4(2+1)² / 3(1)² is:

12

So the answer to the original expression is 12, either as a simplified fraction or a decimal.