To simplify the expression [tex]\(\frac{\frac{2}{5} - 1}{2 + \frac{5}{4}}\)[/tex], follow these steps:
### Step 1: Simplify the numerator
Simplify the numerator [tex]\(\frac{2}{5} - 1\)[/tex]:
[tex]\[
\frac{2}{5} - 1 = \frac{2}{5} - \frac{5}{5} = \frac{2 - 5}{5} = \frac{-3}{5} = -0.6
\][/tex]
### Step 2: Simplify the denominator
Simplify the denominator [tex]\(2 + \frac{5}{4}\)[/tex]:
[tex]\[
2 + \frac{5}{4} = \frac{8}{4} + \frac{5}{4} = \frac{8 + 5}{4} = \frac{13}{4} = 3.25
\][/tex]
### Step 3: Divide the simplified numerator by the simplified denominator
Now, divide the simplified numerator by the simplified denominator:
[tex]\[
\frac{-0.6}{3.25}
\][/tex]
This division can be interpreted as multiplying by the reciprocal:
[tex]\[
-0.6 \times \frac{1}{3.25} \approx -0.18461538461538463
\][/tex]
Thus, the simplified result of the expression [tex]\(\frac{\frac{2}{5} - 1}{2 + \frac{5}{4}}\)[/tex] is approximately [tex]\(-0.1846\)[/tex].