### Instruction: What is the equation of the oblique asymptote of the graph of $\frac{2x^2+7x+10}{2x+3}$?

Enter your answer in the form $y = mx + b.$.### Response: I know that an oblique asymptote is a line that the graph of a rational function approaches as $x$ goes to positive or negative infinity.
To find the equation of the oblique asymptote, I need to divide the numerator by the denominator using long division or synthetic division.
I will use long division because I find it easier to work with.
I start by writing the numerator inside the long division symbol and the denominator outside.
Then I ask myself, how many times does 2x go into 2x^2?
The answer is x, so I write x above the division symbol and multiply x by 2x+3.
I get 2x^2+3x and I subtract it from 2x^2+7x+10.
I get 4x+10 as the remainder.
Then I ask myself, how many times does 2x go into 4x?
The answer is 2, so I write 2 above the division symbol and multiply 2 by 2x+3.
I get 4x+6 and I subtract it from 4x+10.
I get 4 as the final remainder.
This means that $\frac{2x^2+7x+10}{2x+3} = x + 2 + \frac{4}{2x+3}$.
As x goes to positive or negative infinity, the fraction $\frac{4}{2x+3}$ goes to zero, so the graph approaches the line $y = x + 2$.
This is the equation of the oblique asymptote.