To determine which student correctly subtracted the given rational expressions:
[tex]\[
\frac{1}{a-1}-\frac{1}{\pi^\pi+2\pi-5}
\][/tex]
Let's analyze each student's work step-by-step:
1. Steve:
[tex]\[
\frac{1}{x-1} - \frac{3}{(x-1)(x+3)} = \frac{1(x+3) - 3}{(x-1)(x+3)} = \frac{x}{(x-1)(x+3)}
\][/tex]
Steve simplifies to:
[tex]\[
\frac{x}{(x-1)(x+3)}
\][/tex]
2. Emma:
[tex]\[
\frac{1}{x-1} - \frac{3}{(x-1)(x+3)} = \frac{1(x+3) + 3}{(z-1)(z+3)} = \frac{z+6}{(z-1)(z+3)}
\][/tex]
Emma simplifies to:
[tex]\[
\frac{z+6}{(z-1)(z+3)}
\][/tex]
3. Maria:
[tex]\[
\frac{1}{x-1} - \frac{3}{(x-1)(x+3)} = \frac{1(x+3) - 3}{(x-1)(x+3)} = \frac{-2}{x+3}
\][/tex]
Maria simplifies to:
[tex]\[
\frac{-2}{x+3}
\][/tex]
4. George:
[tex]\[
\frac{1-3}{x-1-x^3-2x+3} = \frac{-2}{-x^1-x+2}
\][/tex]
We recognize that in the problem [tex]\(\frac{1}{a-1}-\frac{1}{\pi^\pi+2\pi-5}\)[/tex], the exact constants and expressions are unique and challenging to simplify accurately.
Upon evaluating and comparing the steps followed by each student with the required rational expression subtraction, we notice that:
- Steve's and Maria's simplifications involved polynomials, but they changed the form and terms significantly.
- Emma and George both included errors as well.
- The required result must lead to a specific corrected fraction that aligns precisely with subtracting the given fractions.
After analyzing all provided attempts, none of the solutions matched perfectly or provided a valid step-by-step reduction that aligns with [tex]\(\frac{1}{a-1}-\frac{1}{\pi^\pi+2\pi-5}\)[/tex] in terms of subtraction and combination.
Therefore, no student provided the correct subtraction for the given rational expressions.
