In the future, please be careful about parentheses. I suspect you meant: (3x^2 + 2x)/(x - 1) - (10x - 5)/(x - 1).
The thing to remember about elementary algebra is that the letters and expressions just stand for ordinary numbers. So everything you learned in arithmetic applies in elementary algebra.
\(\displaystyle \dfrac{8}{11} - \dfrac{5}{11} = \dfrac{3}{11}.\)
The rule you learned in arithmetic about subtracting two fractions with a COMMON denominator was: \(\displaystyle \dfrac{a}{b} - \dfrac{c}{b} = \dfrac{a - c}{b}.\)
So, yes, in the problem that you asked about, you simply subtract the numerators because the denominator of both fractions is the same.
\(\displaystyle \dfrac{3x^2 + 2x}{x - 1} - \dfrac{10x - 5}{x - 1} = \dfrac{3x^2 - 8x + 5}{x - 1}.\)
Question: can you simplify that expression?
