To simplify the expression [tex]\(\frac{3}{2} + \left(-\frac{6}{5}\right)\)[/tex], let's follow these steps:
1. Identify a common denominator: First, identify the least common denominator (LCD) for the fractions [tex]\(\frac{3}{2}\)[/tex] and [tex]\(-\frac{6}{5}\)[/tex]. The denominators are 2 and 5. The LCD of 2 and 5 is 10.
2. Rewrite each fraction with the common denominator:
- For [tex]\(\frac{3}{2}\)[/tex], multiply the numerator and the denominator by 5 to get:
[tex]\[
\frac{3 \times 5}{2 \times 5} = \frac{15}{10}
\][/tex]
- For [tex]\(-\frac{6}{5}\)[/tex], multiply the numerator and the denominator by 2 to get:
[tex]\[
\frac{-6 \times 2}{5 \times 2} = \frac{-12}{10}
\][/tex]
3. Add the fractions: Now that they have the same denominator, you can add the numerators and keep the common denominator:
[tex]\[
\frac{15}{10} + \frac{-12}{10} = \frac{15 + (-12)}{10} = \frac{3}{10}
\][/tex]
Thus, the result after simplifying [tex]\(\frac{3}{2} + \left(-\frac{6}{5}\right)\)[/tex] is:
[tex]\[
\frac{3}{10}
\][/tex]
