Certainly! Let's break down the given expression and solve it step by step:
The expression we need to simplify is:
[tex]$\frac{15-[8-(2+5)]}{18-5^2}$[/tex]
1. Solve the innermost parentheses first:
[tex]\[
2 + 5 = 7
\][/tex]
2. Substitute this result back into the expression:
[tex]\[
8 - 7
\][/tex]
3. Solve the expression within the brackets:
[tex]\[
8 - 7 = 1
\][/tex]
4. Substitute this back into the original expression:
[tex]\[
15 - 1
\][/tex]
5. Solve the numerator:
[tex]\[
15 - 1 = 14
\][/tex]
6. Now, address the denominator, starting with the exponentiation:
[tex]\[
5^2 = 25
\][/tex]
7. Substitute this into the denominator expression:
[tex]\[
18 - 25
\][/tex]
8. Solve the denominator:
[tex]\[
18 - 25 = -7
\][/tex]
9. Finally, compute the overall fraction:
[tex]\[
\frac{14}{-7} = -2.0
\][/tex]
Putting it all together, the step-by-step solution to the expression is:
[tex]\[
\frac{15-[8-(2+5)]}{18-5^2} = \frac{14}{-7} = -2.0
\][/tex]
Thus, the final result is:
[tex]\[
-2.0
\][/tex]
