Simplify: [tex]$\frac{6 x^5-2 x-4}{2 x}$[/tex]
Answer (2)
Divide each term in the numerator by 2 x .
Simplify 2 x 6 x 5 to 3 x 4 .
Simplify 2 x 2 x to 1 .
Simplify 2 x 4 to x 2 . The final simplified expression is 3 x 4 − 1 − x 2 .
Explanation
Understanding the Problem We are given the expression 2 x 6 x 5 − 2 x − 4 and our goal is to simplify it. We will divide each term in the numerator by the denominator, 2 x .
Separating the Fraction We can rewrite the expression as: 2 x 6 x 5 − 2 x 2 x − 2 x 4
Simplifying Each Term Now, let's simplify each term individually:
2 x 6 x 5 = 3 x 5 − 1 = 3 x 4
2 x 2 x = 1
2 x 4 = x 2
Final Simplified Expression Putting it all together, we have: 3 x 4 − 1 − x 2 So, the simplified expression is 3 x 4 − 1 − x 2 .
Examples
Imagine you are a software engineer and you have a complex calculation to perform repeatedly in your code. Simplifying the expression beforehand, like we did here, can significantly reduce the computational load and make your program run faster. This is especially important in performance-critical applications such as game development or financial modeling, where every millisecond counts.
To simplify the expression 2 x 6 x 5 − 2 x − 4 , we divide each term of the numerator by 2 x . The final result is 3 x 4 − 1 − x 2 .
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