To solve the given expression [tex]\(\frac{2\left(\frac{4}{5} x\right)}{\left(120+\frac{1}{3} x\right)}(0.6 x)\)[/tex], let's go through it step-by-step:
1. Simplifying the numerator:
[tex]\[
\frac{2\left(\frac{4}{5} x\right)}{\left(120+\frac{1}{3} x\right)}(0.6 x)
\][/tex]
First, simplify the part inside the numerator:
[tex]\[
2 \left(\frac{4}{5} x\right) = \frac{8}{5} x
\][/tex]
The expression now becomes:
[tex]\[
\frac{\frac{8}{5} x}{120+\frac{1}{3} x}(0.6 x)
\][/tex]
2. Combining terms:
Now, we need to rewrite the fraction as a single fraction:
[tex]\[
\frac{\left(\frac{8}{5} x\right) \cdot (0.6 x)}{120 + \frac{1}{3} x}
\][/tex]
Multiplying the terms in the numerator:
[tex]\[
\frac{8}{5} x \cdot 0.6x = \frac{8}{5} \cdot 0.6 x^2 = 1.6 x^2
\][/tex]
Modifying the expression:
[tex]\[
\frac{1.6 x^2}{120 + \frac{1}{3} x}
\][/tex]
3. Simplifying the denominator:
Now, let's rewrite the denominator for clarity:
[tex]\[
120 + \frac{1}{3} x
\][/tex]
This part stays unchanged.
4. Final simplified form:
Now, let's put it all together into a single fraction:
[tex]\[
\frac{1.6 x^2}{120 + \frac{1}{3} x}
\][/tex]
After reviewing the steps and ensuring accuracy, the final simplified answer is:
[tex]\[
\frac{0.96 x^2}{0.333333333333333 x + 120}
\][/tex]
