Let's break down the given expression and solve it step-by-step:
[tex]\[
\frac{(2.5)^2 + 2 \times 2.5 \times 1.4 + (1.4)^2}{2.5 + 1.4}
\][/tex]
### Step 1: Calculate [tex]\((2.5)^2\)[/tex]
First, we need to square 2.5:
[tex]\[
(2.5)^2 = 2.5 \times 2.5 = 6.25
\][/tex]
### Step 2: Calculate [tex]\(2 \times 2.5 \times 1.4\)[/tex]
Next, we calculate the product of 2, 2.5, and 1.4:
[tex]\[
2 \times 2.5 \times 1.4 = 2 \times 3.5 = 7.0
\][/tex]
### Step 3: Calculate [tex]\((1.4)^2\)[/tex]
Then, we square 1.4:
[tex]\[
(1.4)^2 = 1.4 \times 1.4 = 1.96
\][/tex]
### Step 4: Sum up the results from steps 1, 2, and 3 for the numerator
Now, we add together the results from steps 1, 2, and 3 to get the numerator:
[tex]\[
6.25 + 7.0 + 1.96 = 15.21
\][/tex]
### Step 5: Calculate the denominator
Next, we add 2.5 and 1.4 for the denominator:
[tex]\[
2.5 + 1.4 = 3.9
\][/tex]
### Step 6: Divide the numerator by the denominator
Finally, we divide the numerator by the denominator to find the result:
[tex]\[
\frac{15.21}{3.9} = 3.9
\][/tex]
### Summary:
The detailed step-by-step solution gives us:
- Numerator: [tex]\(15.21\)[/tex]
- Denominator: [tex]\(3.9\)[/tex]
- Result: [tex]\(3.9\)[/tex]
So, the value of the expression is [tex]\(3.9\)[/tex].
