How do you divide #(x^2 + x - 6)/(2x-2)#?

Question

Kennedy Adams · Accepted Answer

This is a rational exponant division problem.

Thus, you have to first factor both the numerator and denominator. #((x-2)(x+3))/(2(x-1)# Since, you can't simplify the fraction any furthur, this should be your answer. You should also include the restrictions. The restrictions should include any instances where the denominator is zero. In this case, the restriction is 1.

Eva Adamson · Answer

undefined To divide (x^2 + x - 6) by (2x - 2), you can use polynomial long division. Here are the steps:

1. Divide the first term of the numerator (x^2) by the first term of the denominator (2x). The result is (1/2)x.

2. Multiply the entire denominator (2x - 2) by the result from step 1, which is (1/2)x. This gives you (1/2)x(2x - 2) = x^2 - x.

3. Subtract the result from step 2 from the numerator (x^2 + x - 6). This gives you (x^2 + x - 6) - (x^2 - x) = 2x - 6.

4. Bring down the next term from the numerator, which is -6.

5. Divide the first term of the new numerator (2x) by the first term of the denominator (2x). The result is 1.

6. Multiply the entire denominator (2x - 2) by the result from step 5, which is 1. This gives you 1(2x - 2) = 2x - 2.

7. Subtract the result from step 6 from the new numerator (2x - 6). This gives you (2x - 6) - (2x - 2) = -4.

8. Since there are no more terms in the numerator, the division is complete.

The quotient is (1/2)x + 1 and the remainder is -4.