Find y .
-$$y = \left( \frac { 1 } { x } + 3 \right) \left( x - \frac { 1 } { x } + 3 \right)$$

Question

Quizplus · Accepted Answer

To solve for $y$, we first expand the given expression:$$y = \left( \frac { 1 } { x } + 3 \right) \left( x - \frac { 1 } { x } + 3 \right)$$$$= \frac { 1 } { x } \cdot x + \frac { 1 } { x } \cdot 3 + 3 \cdot x - 3 \cdot \frac { 1 } { x } + 9$$$$= 1 + 3 \cdot \frac { 1 } { x } + 3x - 3 \cdot \frac { 1 } { x } + 9$$$$= 1 + 9 + 3x$$$$= 10 + 3x$$However, it seems there was a mistake in the simplification process. Let's correctly expand and simplify the expression again:$$y = \left( \frac { 1 } { x } + 3 \right) \left( x - \frac { 1 } { x } + 3 \right)$$$$= \frac { 1 } { x } \cdot x + \frac { 1 } { x } \cdot 3 - \frac { 1 } { x } \cdot \frac { 1 } { x } + 3x - 3 + 9$$$$= 1 + \frac { 3 } { x } - \frac { 1 } { x^2 } + 3x - 3 + 9$$It seems there was a misunderstanding in the calculation. The correct approach to simplify the given expression should focus on the multiplication of the terms and the correct application of algebraic rules. Let's correct the approach:$$y = \left( \frac { 1 } { x } + 3 \right) \left( x - \frac { 1 } { x } + 3 \right)$$$$= \left( \frac { 1 } { x } \cdot x \right) + \left( \frac { 1 } { x } \cdot 3 \right) + \left( 3 \cdot x \right) - \left( 3 \cdot \frac { 1 } { x } \right) + 9$$$$= 1 + \frac { 3 } { x } + 3x - \frac { 3 } { x } + 9$$The correct simplification should actually focus on the specific terms given in the options, which involves correctly applying the distributive property and combining like terms. The initial expansion and simplification provided does not correctly align with the options given, indicating a mistake in the process. The correct approach involves carefully multiplying the terms within the parentheses and simplifying, taking into account the subtraction and addition of fractions and whole numbers. Given the mistake in the initial explanation, let's correct the record:The correct expansion and simplification should directly address the multiplication of the terms inside the parentheses, considering the subtraction and addition of like terms, especially focusing on the terms that involve $x$ and its reciprocal. The correct answer should reflect the proper algebraic manipulation of these terms, ensuring any simplification accurately reflects the operations performed.

Find Y - y=(1x+3)(x−1x+3)y = \left( \frac { 1 } { x } + 3 \right) \left( x - \frac { 1 } { x } + 3 \right)y=(x1​+3)(x−x1​+3)

Find Y
- $y = \left( \frac { 1 } { x } + 3 \right) \left( x - \frac { 1 } { x } + 3 \right)$