Question

Explain in words how (2²-6/x³-2²+3-6) can be simplified to (2+3/x²+3).

Answer 1

To simplify (2²-6/x³-2²+3-6) to (2+3/x²+3), first simplify the exponents, then combine like terms, and finally write the expression with a common denominator.

Step-by-step explanation:

To simplify the expression (2²-6/x³-2²+3-6) to (2+3/x²+3), we need to follow the order of operations and combine like terms. Here are the steps:

1. Simplify the exponents: 2² = 4 and 2² = 4.
2. Simplify the division: 6/x³ = 6x^(-3).
3. Combine like terms: 4 + 4 - 6x^(-3) + 3 - 6 = 5 - 6x^(-3).
4. Write the expression with a common denominator: 5 - 6x^(-3) = (5x^3 - 6)/(x^3).
5. Cross-multiply to simplify: (5x^3 - 6)/(x^3) = (5 + 6x^3)/(x^3).

So, the simplified expression is (2+3/x²+3).