### Instruction: What is the simplified numerical value of $\frac{a+11b}{a-b}$ if $\frac{4a+3b}{a-2b}=5$?### Response: To simplify the first expression, I need to find the values of $a$ and $b$ in terms of each other.
One way to do that is to use the second equation and solve for one of the variables.
I can try to isolate $a$ by multiplying both sides by $a-2b$ and then expanding and rearranging the terms.
I get $4a+3b=5a-10b$, which simplifies to $a=13b$.
Now I can substitute this into the first expression and simplify it further.
I get $\frac{a+11b}{a-b}=\frac{13b+11b}{13b-b}$.
This simplifies to $\frac{24b}{12b}=\frac{24}{12}$.
This is a familiar fraction that I can simplify by dividing the numerator and denominator by 12.