Question

question #10 perform the indicated operation for the given rational expressions: $\frac{2y - 5}{y^{2}-6}-\frac{y - 2}{y^{2}-6}$. write the answer in simplest form. $\frac{3y - 3}{y^{2}-6}$ $\frac{y - 3}{y^{2}-6}$ $\frac{3y - 7}{y^{2}-6}$ $\frac{y - 7}{2y^{2}-12}$

Explanation:

Step1: Subtract numerators

Since the denominators are the same ($y^{2}-6$), we subtract the numerators: $(2y - 5)-(y - 2)$.
$(2y-5)-(y - 2)=2y-5 - y+2$.

Step2: Combine like - terms

Combine the $y$ terms and the constant terms: $2y-y-5 + 2=y-3$.
The resulting rational expression is $\frac{y - 3}{y^{2}-6}$.

Answer:

$\frac{y - 3}{y^{2}-6}$ (corresponding to the second option in the multiple - choice list)