Let's solve the given mathematical expression step by step:
[tex]\[
\frac{20}{0^2+30+1} + \frac{20-1}{(\theta+2)}
\][/tex]
1. Evaluate the first fraction:
[tex]\[
\frac{20}{0^2 + 30 + 1}
\][/tex]
- Calculate the denominator:
[tex]\[
0^2 + 30 + 1 = 0 + 30 + 1 = 31
\][/tex]
- So the first fraction becomes:
[tex]\[
\frac{20}{31}
\][/tex]
This can be approximately written as:
[tex]\[
\frac{20}{31} \approx 0.6451612903225806
\][/tex]
2. Evaluate the second fraction:
[tex]\[
\frac{20-1}{(\theta+2)}
\][/tex]
- Simplify the numerator:
[tex]\[
20 - 1 = 19
\][/tex]
- For this calculation, let's assume that the value of [tex]\(\theta\)[/tex] is 1. Then, the denominator becomes:
[tex]\[
1 + 2 = 3
\][/tex]
- So the second fraction becomes:
[tex]\[
\frac{19}{3}
\][/tex]
This can be approximately written as:
[tex]\[
\frac{19}{3} \approx 6.333333333333333
\][/tex]
3. Sum the two fractions:
[tex]\[
0.6451612903225806 + 6.333333333333333
\][/tex]
- Adding these together:
[tex]\[
0.6451612903225806 + 6.333333333333333 = 6.978494623655914
\][/tex]
So, the detailed step-by-step solution for the expression
[tex]\[
\frac{20}{0^2+30+1}+\frac{20-1}{(\theta+2)}
\][/tex]
with [tex]\(\theta = 1\)[/tex] is:
- First fraction: [tex]\( \frac{20}{31} \approx 0.6451612903225806 \)[/tex]
- Second fraction: [tex]\( \frac{19}{3} \approx 6.333333333333333 \)[/tex]
- Sum of the fractions: [tex]\( 0.6451612903225806 + 6.333333333333333 = 6.978494623655914 \)[/tex]
Thus, the final result is:
[tex]\[
6.978494623655914
\][/tex]
