`((2)/(3)a^(2)-(4)/(9)a^(2))/(2a)=4` where `ane0`
What is the value of a in the expression above,

Options

A. 28
B. 42
C. 36
D. 12

Answer

To solve the equation \(\frac{\frac{2}{3}a^{2} - \frac{4}{9}a^{2}}{2a} = 4\), we will follow these steps:

### Step 1: Simplify the numerator
First, we need to simplify the expression in the numerator:
\[ \frac{2}{3}a^{2} - \frac{4}{9}a^{2} \]
To do this, we need a common denominator. The common denominator of 3 and 9 is 9.

Rewriting \(\frac{2}{3}a^{2}\) with a denominator of 9:
\[ \frac{2}{3}a^{2} = \frac{6}{9}a^{2} \]
Now, substituting back into the expression:
\[ \frac{6}{9}a^{2} - \frac{4}{9}a^{2} = \frac{6 - 4}{9}a^{2} = \frac{2}{9}a^{2} \]

### Step 2: Rewrite the equation
Now we can rewrite the original equation:
\[ \frac{\frac{2}{9}a^{2}}{2a} = 4 \]

### Step 3: Simplify the left-hand side
Now, simplify the left-hand side:
\[ \frac{2}{9}a^{2} \div 2a = \frac{2}{9}a^{2} \cdot \frac{1}{2a} = \frac{2a^{2}}{18a} = \frac{a}{9} \]
So we have:
\[ \frac{a}{9} = 4 \]

### Step 4: Solve for \(a\)
To find \(a\), multiply both sides by 9:
\[ a = 4 \times 9 = 36 \]

### Step 5: Conclusion
Thus, the value of \(a\) is:
\[ \boxed{36} \]

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