I assume the poster was trying to type "oblique asymptote"
from your answer of 3x+2 + 7/(x-1) we can conclude that there is an oblique linear asymptote of y = 3x + 2, and a vertical asymptote at x = 1 for the original function given.
how do u find obblique symptotes? i know its long division but how do u divide something like 3x^2-x+5 divided by x-1? please help me... thanks!
I don't know what an oblique "symptote" is, but you to polynomial long division the same wau you do it with numbers.
The first term of (3x^2 - x + 5)/(x-1) is 3x. Multiply that by x-1 and put the product under the dividend, and subtract. You'll get 2x + 5. x+1 goes into that 2 times, but there will be a remainder. The answer will be
3x + 2 + 7/(x-1)
To find the oblique asymptote of a rational function, you can use polynomial long division. Here's how you would divide the polynomial 3x^2 - x + 5 by the linear polynomial x - 1:
1. Write the dividend and divisor in the long division format:
______________________________________
x - 1 | 3x^2 - x + 5
2. Start dividing by considering the highest degree term in the dividend (3x^2) divided by the highest degree term in the divisor (x). This gives you the first term of the quotient, which is 3x. Write this term above the line.
3x
______________________________________
x - 1 | 3x^2 - x + 5
3. Multiply the divisor (x - 1) by the first term of the quotient (3x) and write the product beneath the dividend:
3x
______________________________________
x - 1 | 3x^2 - x + 5
- (3x^2 - 3x)
4. Subtract the product from the dividend and bring down the next term (- x in this case):
3x
______________________________________
x - 1 | 3x^2 - x + 5
- (3x^2 - 3x)
__________
2x + 5
5. Now, consider the highest degree term in the new remainder (2x) divided by the highest degree term in the divisor (x). This gives you the second term of the quotient, which is 2. Write this term next to the first term of the quotient.
3x + 2
______________________________________
x - 1 | 3x^2 - x + 5
- (3x^2 - 3x)
__________
2x + 5
6. Multiply the divisor (x - 1) by the second term of the quotient (2) and write the product beneath the remainder:
3x + 2
______________________________________
x - 1 | 3x^2 - x + 5
- (3x^2 - 3x)
__________
2x + 5
- (2x - 2)
_______
7
7. Subtract the product from the remainder and you will get a constant term of 7.
3x + 2 + 7/(x - 1)
______________________________________
x - 1 | 3x^2 - x + 5
- (3x^2 - 3x)
__________
2x + 5
- (2x - 2)
_______
7
So, the result of the polynomial long division is 3x + 2 + 7/(x - 1). This means that the oblique asymptote of the function 3x^2 - x + 5 divided by x - 1 is the equation y = 3x + 2.