I know it's easy, but I totally just blanked out on how to divide rational expressions. We're supposed to write them in the form quotient + (remainder/Divisor)
For example, (2h2+h-2)/(h2-1)
Those are h squareds. I know you would take h2 into 2h2 and get 2, but then I'm thinking you'd multiply h2-1 by 2 and subtract that from the numerator, but that doesn't work.
yes. When you multiply h^2 - 1 by 2, you get 2h^2 - 2. Thus, the remainder is h. Thus, the answer is
2 with remainder of h/(h^2-1)
To divide rational expressions, you can use a method called polynomial long division. Here's how you can solve the example you provided:
1. Start by writing the dividend (numerator) and the divisor (denominator) in the long division format, with the numerator inside the division symbol and the denominator outside the division symbol.
(2h^2 + h - 2) ÷ (h^2 - 1)
2. Begin dividing the first term of the numerator by the first term of the denominator. In this case, divide 2h^2 by h^2. The result is 2. Write this as the quotient above the long division symbol.
2
-------
h^2 - 1 | 2h^2 + h - 2
3. Multiply the entire divisor (h^2 - 1) by the quotient you just obtained (2), and write it below the numerator, aligned with the like terms.
2h^2 - 2
-------------
h^2 - 1 | 2h^2 + h - 2
4. Subtract the multiplied portion from the original numerator.
2h^2 - 2
-------------
h^2 - 1 | 2h^2 + h - 2
- (2h^2 - 2)
-------------
3h - 2
5. Bring down the next term from the numerator, which is 3h.
2h^2 - 2
-------------
h^2 - 1 | 2h^2 + h - 2
- (2h^2 - 2)
-------------
3h - 2
-------
3h
6. Repeat steps 3 to 5 with the new numerator (3h).
2h^2 - 2 + 3h
------------------
h^2 - 1 | 2h^2 + h - 2
- (2h^2 - 2)
---------------
3h - 2
--------
3h + 2
7. Since there are no more terms remaining in the numerator, the division is complete. The quotient is 2 + (3h + 2)/(h^2 - 1).
Therefore, the result of dividing (2h^2 + h - 2) by (h^2 - 1) is 2 + (3h + 2)/(h^2 - 1).