Multiply. Write your answer in simplest form. 2x - 3/x^2 * (4x + 1) ______

Identify Terms: Identify the terms to be multiplied. We have the fraction (2x - 3)/x^2 and the binomial (4x + 1). To multiply these, we will apply the distributive property.Multiply Numerator: Multiply the numerator of the fraction by the binomial. This means we will distribute (2x - 3) across (4x + 1). Calculation: (2x - 3) * (4x + 1) = 2x * 4x + 2x * 1 - 3 * 4x - 3 * 1Perform Multiplication: Perform the multiplication from Step 2. Calculation: 2x * 4x + 2x * 1 - 3 * 4x - 3 * 1 = 8x^2 + 2x - 12x - 3Combine Like Terms: Combine like terms in the result from Step 3. Calculation: 8x^2 + 2x - 12x - 3 = 8x^2 - 10x - 3Place Over Denominator: Place the result from Step 4 over the original denominator x^2. Calculation: (8x^2 - 10x - 3) / x^2Simplify Expression: Simplify the expression by dividing each term in the numerator by x^2. Calculation: 8x^2/x^2 - 10x/x^2 - 3/x^2 = 8 - 10/x - 3/x^2Write Final Answer: Write the final answer in simplest form. The expression is already simplified as each term is divided by x^2. Final Answer: 8 - 10/x - 3/x^2

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Algebra 1

Multiply and divide rational expressions

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Q. Multiply. Write your answer in simplest form.

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\frac{2x - 3}{x^2} \times (4x + 1)

Identify Terms: Identify the terms to be multiplied. We have the fraction $(2x - 3)/x^2$ and the binomial $(4x + 1)$ . To multiply these, we will apply the distributive property.
Multiply Numerator: Multiply the numerator of the fraction by the binomial. This means we will distribute $(2x - 3)$ across $(4x + 1)$ . $\newline$ Calculation: $(2x - 3) * (4x + 1) = 2x * 4x + 2x * 1 - 3 * 4x - 3 * 1$
Perform Multiplication: Perform the multiplication from Step $2$ . $\newline$ Calculation: $2x \times 4x + 2x \times 1 - 3 \times 4x - 3 \times 1 = 8x^2 + 2x - 12x - 3$
Combine Like Terms: Combine like terms in the result from Step $3$ . $\newline$ Calculation: $8x^2 + 2x - 12x - 3 = 8x^2 - 10x - 3$
Place Over Denominator: Place the result from Step $4$ over the original denominator $x^2$ . $\newline$ Calculation: $(8x^2 - 10x - 3) / x^2$
Simplify Expression: Simplify the expression by dividing each term in the numerator by $x^2$ . $\newline$ Calculation: $\frac{8x^2}{x^2} - \frac{10x}{x^2} - \frac{3}{x^2} = 8 - \frac{10}{x} - \frac{3}{x^2}$
Write Final Answer: Write the final answer in simplest form. The expression is already simplified as each term is divided by $x^2$ . $\newline$ Final Answer: $8 - \frac{10}{x} - \frac{3}{x^2}$