To solve the expression \( \frac{1.487^3 - 1}{1.487^3 + 1} \), we can start by calculating \( 1.487^3 \).
Step 1: Calculate \( 1.487^3 \)
Calculating \( 1.487^3 \):
\[ 1.487^3 \approx 3.303741 \]
Step 2: Substitute into the expression
Now substitute \( 1.487^3 \) into our expression:
\[ \frac{1.487^3 - 1}{1.487^3 + 1} = \frac{3.303741 - 1}{3.303741 + 1} \]
Step 3: Simplify the numerator and denominator
Calculating the numerator and the denominator:
\[ 3.303741 - 1 = 2.303741 \] \[ 3.303741 + 1 = 4.303741 \]
Step 4: Final Calculation
Now substitute the values back into the fraction:
\[ \frac{2.303741}{4.303741} \]
Calculating this value gives:
\[ \frac{2.303741}{4.303741} \approx 0.5351 \]
Conclusion
Thus, the value of \( \frac{1.487^3 - 1}{1.487^3 + 1} \) is approximately \( 0.5351 \).