Divide and simplify.
1. 2y^2 - 7y + 3/2y^2 + 3y - 2 divided by 6y^2 - 5y + 1/3y^2 + 5y -2
2. x^2 + 13x + 12/x + 2 divided by
(x + 1)
Please explain! Thanks!
mosey on over to calc101.com and click on the "long division" link. It will let you divide polynomials and shows all the details.
To divide and simplify the given expressions, follow these steps:
1. Factor both the numerator and denominator of the dividend and the divisor, if possible.
2. Simplify by canceling out any common factors.
3. Multiply the reciprocal of the divisor to find the result.
Let's solve each division problem step by step:
1. For the first problem:
Dividend: 2y^2 - 7y + 3/2y^2 + 3y - 2
Divisor: 6y^2 - 5y + 1/3y^2 + 5y - 2
Factor both the dividend and divisor:
Dividend factors to: (2y - 1)(y - 3)
Divisor factors to: (6y - 1)(y - 2)
Now, we can simplify by canceling out common factors. In this case, there are no common factors between the numerator and the denominator.
Multiply the reciprocal of the divisor:
Dividend x Reciprocal of Divisor = (2y - 1)(y - 3) / [(6y - 1)(y - 2)]
This is the simplified expression.
2. For the second problem:
Dividend: x^2 + 13x + 12 / x + 2
Divisor: x + 1
First, notice that the dividend is already factored, so we don't need to make any further factorization. We can proceed with simplifying.
Cancel out the common factors:
x^2 + 13x + 12 = (x + 1)(x + 12)
Now, you can multiply the reciprocal of the divisor:
Dividend x Reciprocal of Divisor = (x + 1)(x + 12) / (x + 1)
Simplifying further, the common factor (x + 1) cancels out, leaving us with:
Result = x + 12
This is the simplified expression.
Remember, always check for common factors and then multiply by the reciprocal of the divisor to get the simplified form in division problems.