The value of `( 4 x ^(3) - x)/( ( 2 x + 1) ( 6 x - 3))` when x = 9999 is

Options

A. 1111
B. 2222
C. 3333
D. 6666

Answer

To solve the expression \(( 4x^3 - x)/(( 2x + 1)( 6x - 3))\) when \(x = 9999\), we can follow these steps:

### Step 1: Simplify the numerator

The numerator is \(4x^3 - x\). We can factor out \(x\):

\[ 4x^3 - x = x(4x^2 - 1) \]

### Step 2: Factor the expression further

Notice that \(4x^2 - 1\) can be factored using the difference of squares:

\[ 4x^2 - 1 = (2x + 1)(2x - 1) \]

So, the numerator becomes:

\[ x(4x^2 - 1) = x(2x + 1)(2x - 1) \]

### Step 3: Rewrite the entire expression

Now we can rewrite the entire expression:

\[ \frac{x(2x + 1)(2x - 1)}{(2x + 1)(6x - 3)} \]

### Step 4: Cancel common factors

We can cancel the common factor \((2x + 1)\) from the numerator and denominator:

\[ \frac{x(2x - 1)}{6x - 3} \]

### Step 5: Factor the denominator

The denominator \(6x - 3\) can be factored as:

\[ 6x - 3 = 3(2x - 1) \]

So the expression now looks like:

\[ \frac{x(2x - 1)}{3(2x - 1)} \]

### Step 6: Cancel the common factors again

We can cancel \((2x - 1)\) from the numerator and denominator (as long as \(x \neq \frac{1}{2}\)):

\[ \frac{x}{3} \]

### Step 7: Substitute \(x = 9999\)

Now we substitute \(x = 9999\):

\[ \frac{9999}{3} = 3333 \]

### Final Answer

The value of the expression when \(x = 9999\) is:

\[ \boxed{3333} \]

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