Perform the operation and simplify the answer fully. (x^(2))/(2)÷(5x)/(2) Answer:

Rewrite Division as Multiplication: Rewrite the division as multiplication by the reciprocal. To divide by a fraction, you multiply by its reciprocal. The reciprocal of (5x)/(2) is (2)/(5x).Set Up the Multiplication: Set up the multiplication. ((x^2)/2) * (2/(5x)) is the multiplication we need to perform.Multiply Numerators and Denominators: Multiply the numerators and denominators. (x^2 * 2) / (2 * 5x) simplifies to (2x^2) / (10x).Simplify the Expression: Simplify the expression. We can cancel out a factor of 2 and x from the numerator and denominator. (2x^2) / (10x) simplifies to (x^2) / (5x).Cancel Common Factor: Cancel the common factor of x. (x^2) / (5x) simplifies to x/5 after canceling out one x from the numerator and denominator.

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Find derivatives of using multiple formulae

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Q. Perform the operation and simplify the answer fully.

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\frac{x^{2}}{2} \div \frac{5 x}{2}

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Answer:

Rewrite Division as Multiplication: Rewrite the division as multiplication by the reciprocal. $\newline$ To divide by a fraction, you multiply by its reciprocal. The reciprocal of $(5x)/(2)$ is $(2)/(5x)$ .
Set Up the Multiplication: Set up the multiplication. $\left(\frac{x^2}{2}\right) \times \left(\frac{2}{5x}\right)$ is the multiplication we need to perform.
Multiply Numerators and Denominators: Multiply the numerators and denominators. $(x^2 \times 2) / (2 \times 5x)$ simplifies to $(2x^2) / (10x)$ .
Simplify the Expression: Simplify the expression. $\newline$ We can cancel out a factor of $2$ and $x$ from the numerator and denominator. $\newline$ $(2x^2) / (10x)$ simplifies to $(x^2) / (5x)$ .
Cancel Common Factor: Cancel the common factor of $x$ . $\newline$ $\frac{x^2}{5x}$ simplifies to $\frac{x}{5}$ after canceling out one $x$ from the numerator and denominator.