Question

Express the result of each division problem below in simplest form.

(5x³-10x²)/10x²+40x + (x²-5x+6)/x²+x-12

Answer 1

To divide the given expression, use long division to simplify the given expression step by step.

Step-by-step explanation:

To divide the given expression, we can use the technique of long division. Here are the steps:

1. Arrange the terms of the numerator and denominator in descending order of their degrees.
2. Divide the first term of the numerator by the first term of the denominator to get the first term of the quotient.
3. Multiply the first term of the denominator with the entire quotient and subtract it from the numerator.
4. Repeat steps 2 and 3 until all terms have been divided.
5. Simplify the resulting quotient.

Applying these steps to the given problem:

(5x³-10x²)/(10x²+40x) + (x²-5x+6)/(x²+x-12)

• Dividing the first term, we get 5x.
• Multiplying 5x with (10x²+40x) and subtracting it from (5x³-10x²), we get -100x³-100x².
• Dividing the next term (-100x³), we get -10x².
• Multiplying -10x² with (10x²+40x) and subtracting it from (-100x³-100x²), we get -200x²-400x.
• Dividing the last term (-200x²), we get -20x.
• Multiplying -20x with (10x²+40x) and subtracting it from (-200x²-400x), we get 0, since the numerator becomes zero.

So, the simplified form of the division problem is 5x - 10.