Question
Simplify. Express your answer as a single fraction in simplest form.
c
2c–1
–
c
1–2c
c
2c–1
–
c
1–2c
Answers
GPT-4o mini
To simplify the expression
\[
\frac{c}{2c-1} - \frac{c}{1-2c},
\]
we start by rewriting the second fraction:
\[
1 - 2c = -(2c - 1).
\]
So, we can rewrite the expression as:
\[
\frac{c}{2c-1} - \frac{c}{-(2c-1)} = \frac{c}{2c-1} + \frac{c}{2c-1} = \frac{c}{2c-1} + \frac{c}{2c-1} = \frac{c + c}{2c - 1} = \frac{2c}{2c - 1}.
\]
Therefore, the expression simplifies to:
\[
\frac{2c}{2c - 1}.
\]
Since there are no common factors in the numerator and the denominator that we can simplify further, the final answer is:
\[
\frac{2c}{2c - 1}.
\]
\[
\frac{c}{2c-1} - \frac{c}{1-2c},
\]
we start by rewriting the second fraction:
\[
1 - 2c = -(2c - 1).
\]
So, we can rewrite the expression as:
\[
\frac{c}{2c-1} - \frac{c}{-(2c-1)} = \frac{c}{2c-1} + \frac{c}{2c-1} = \frac{c}{2c-1} + \frac{c}{2c-1} = \frac{c + c}{2c - 1} = \frac{2c}{2c - 1}.
\]
Therefore, the expression simplifies to:
\[
\frac{2c}{2c - 1}.
\]
Since there are no common factors in the numerator and the denominator that we can simplify further, the final answer is:
\[
\frac{2c}{2c - 1}.
\]