Question

Simplify by long division
(6y²+ y −2) (2y−1)⁻¹

Answer 1

To simplify (6y² + y - 2) / (2y - 1)⁻¹ using long division, divide the dividend by the divisor. The simplified expression is 3y + 2.

Step-by-step explanation:

To simplify (6y² + y - 2) / (2y - 1)⁻¹ using long division, we divide the dividend (6y² + y - 2) by the divisor (2y - 1). Here are the steps:

1. Start by dividing the first term of the dividend (6y²) by the first term of the divisor (2y). This gives us 3y as the first term of the quotient.
2. Multiply the divisor (2y - 1) by the quotient's first term (3y) to get 6y² - 3y.
3. Subtract the result from the dividend (6y² + y - 2) - (6y² - 3y) = 4y + 2.
4. Bring down the next term of the dividend (-2) and repeat the process.
5. Divide the new dividend (4y + 2) by the first term of the divisor (2y). This gives us 2 as the second term of the quotient.
6. Multiply the divisor (2y - 1) by the quotient's second term (2) to get 4y - 2.
7. Subtract the result from the new dividend (4y + 2) - (4y - 2) = 4.

Therefore, the simplified expression is 3y + 2.