Question - Simplifying a Rational Expression Involving Polynomials
Solution:
\( y = \frac{x}{(2x-1) \cdot (3) \cdot (x-1)} \)
To simplify the expression, factor out and reduce common terms if any.
No common terms to factor out or reduce.
The expression is already in its simplest form. So, the simplified expression is:
\( y = \frac{x}{6x^2 - 3x - 2x + 1} \)
\( y = \frac{x}{6x^2 - 5x + 1} \)
Tutor Solution:
I'd be happy to assist you with this math problem. Let's go through the solution step by step.
The equation provided in the image is:
\[ y = \frac{x}{(2x-1)^3 (x-1)} \]To simplify this expression, we should look for common factors in the numerator and the denominator that could potentially cancel out. However, in this case, there are no common factors to cancel.
Therefore, let's factor the denominator to see if it could be simplified further:
The denominator is already factored, with \((2x-1)^3\) and \((x-1)\). Without common factors in the numerator, the expression is already in its simplest form.
Thus, the simplified form of the given expression is:
\[ y = \frac{x}{(2x-1)^3 (x-1)} \]There isn't much we can do to simplify the expression further without additional information. If we were asked to find the domain of the function, for example, we could proceed by identifying the values of x for which the denominator is zero (since division by zero is undefined).
If you need to find the domain or perform some other operation with this expression, please provide that information so we can continue to work on this problem.
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