Questions: Which of the following expressions is equivalent to 92x^2+x-1+xy+(2x^3)/x? A 94x^2+x+xy-1 B 92x^2+3x+xy-1 C 2x^2+92x+y-1 D 2x^3+92x^2+2x+xy-1

Transcript text: T 5 - Mathematical Knowledge Which of the following expressions is equivalent to $92 x^{2}+x-1+x y+\frac{2 x^{3}}{x}$ ? A $94 x^{2}+x+x y-1$ B $92 x^{2}+3 x+x y-1$ C $2 x^{2}+92 x+y-1$ D $2 x^{3}+92 x^{2}+2 x+x y-1$ Click the button or type the letter to the left of your answer.

Solution

Solution Steps

To simplify the given expression $92x^2 + x - 1 + xy + \frac{2x^3}{x}$, we need to combine like terms and simplify the fraction. The term $\frac{2x^3}{x}$ simplifies to $2x^2$. Adding this to the other $x^2$ term, we get $92x^2 + 2x^2$. The rest of the terms remain unchanged.

Step 1: Simplify the Fraction

First, we simplify the term $\frac{2x^3}{x}$: \[ \frac{2x^3}{x} = 2x^2 \]

Step 2: Combine Like Terms

Next, we combine the like terms in the expression $92x^2 + x - 1 + xy + 2x^2$: \[ 92x^2 + 2x^2 = 94x^2 \]

Step 3: Write the Simplified Expression

After combining the like terms, the simplified expression is: \[ 94x^2 + xy + x - 1 \]