how would i do
(x^2 + 2x) / (2x-1)
thanks
There is not much that can be done to simplify. Factor an x out of the numerator.
x(x+2)/(2x-1)
sio i cant find the quotient of it?
I need to find the qoutient so that i can find the oblique asymptote so i can graph the function.
To simplify the given expression (x^2 + 2x) / (2x-1), we need to perform polynomial long division. Here are the steps:
1. Start by dividing the first term of the numerator by the first term of the denominator. In this case, (x^2) divided by (2x) gives you (1/2) times x, which is (1/2)x. This is the first term of the quotient.
2. Multiply the entire denominator (2x-1) with the first term of the quotient (1/2)x. This gives you (1/2)x * (2x-1) = (1/2)x * 2x + (1/2)x * (-1) = x^2 - (1/2)x.
3. Subtract this result from the numerator (x^2 + 2x) - (x^2 - (1/2)x). Distribute the negative sign, combine like terms, and simplify as follows: x^2 + 2x - x^2 + (1/2)x = (1/2)x + 2x.
4. Continue with the next term of the numerator (1/2)x + 2x, dividing it by the first term of the denominator (2x). (1/2)x divided by (2x) is (1/4), which is the second term of the quotient.
5. Multiply the entire denominator (2x-1) with the second term of the quotient (1/4). This gives you (1/4) * (2x-1) = (1/4) * 2x + (1/4) * (-1) = (1/2)x - (1/4).
6. Subtract this result from the previous result [(1/2)x + 2x] - [(1/2)x - (1/4)]. Distribute the negative sign, combine like terms, and simplify as follows: (1/2)x + 2x - (1/2)x + (1/4) = 2x + (1/4).
Therefore, the simplified form of (x^2 + 2x) / (2x-1) is (1/2)x + 2 + (2x + 1/4) / (2x - 1).
Note: Polynomial long division is more demanding to explain verbally. It may be helpful to search for visual aids or examples to have a more comprehensive understanding.