Solution: Simplification Process Step 1: Combine the terms Start by combining 4x with frac5x + 3 to get 4x cdot frac5x + 3. Step 1.1: Apply multiplication to the constants Multiply the constant 4 with the numerator of the fraction 5 to get x cdot frac4 times 5x + 3. Step 1.2: Simplify the multiplication Carry out the multiplication of the constants to simplify x cdot frac20x + 3. Step 1.3: Merge the variable with the fraction Combine the variable x with the fraction to form fracx times 20x + 3. Step 2: Rearrange the terms Rearrange the terms to place the constant before the variable, resulting in frac20xx + 3. Knowledge Notes: To simplify an algebraic expression like 4x cdot frac5x + 3, we follow these steps: 1. Multiplication of Terms: When multiplying a variable by a fraction, you can directly multiply the variable with the numerator of the fraction, keeping the denominator unchanged. 2. Combining Constants: If there are constants outside the fraction that are being multiplied with the fraction, you can multiply these constants directly with the numerator. 3. Simplification: Always look for opportunities to simplify the expression by combining like terms or reducing fractions if possible. 4. Rearranging Terms: In algebra, it is common to write expressions with constants before variables (e.g., 20x instead of x20). This is more of a convention than a rule, but it helps with readability and standardization. 5. Maintaining the Order of Operations: Remember to follow the order of operations (PEMDAS/BODMAS) when simplifying expressions. Multiplication and division come before addition and subtraction, but any operation enclosed in parentheses should be done first. In this problem, we did not have to use any advanced algebraic techniques such as factoring or expanding because the expression …

Simplify 4x*5/(x+3)

The problem is asking to perform an algebraic simplification on the given expression. The expression is a fraction where the numerator is a product of a constant and a variable (4x times 5), and the denominator is a sum (x plus 3). The task would involve applying the distributive property and/or simplifying any like terms, if possible, to express the result in its simplest form.

$4 x \cdot \frac{5}{x + 3}$

Answer

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Solution:

Simplification Process

Step 1: Combine the terms

Start by combining $4x$ with $\frac{5}{x + 3}$ to get $4x \cdot \frac{5}{x + 3}$.

Step 1.1: Apply multiplication to the constants

Multiply the constant $4$ with the numerator of the fraction $5$ to get $x \cdot \frac{4 \times 5}{x + 3}$.

Step 1.2: Simplify the multiplication

Carry out the multiplication of the constants to simplify $x \cdot \frac{20}{x + 3}$.

Step 1.3: Merge the variable with the fraction

Combine the variable $x$ with the fraction to form $\frac{x \times 20}{x + 3}$.

Step 2: Rearrange the terms

Rearrange the terms to place the constant before the variable, resulting in $\frac{20x}{x + 3}$.

Knowledge Notes:

To simplify an algebraic expression like $4x \cdot \frac{5}{x + 3}$, we follow these steps:

Multiplication of Terms: When multiplying a variable by a fraction, you can directly multiply the variable with the numerator of the fraction, keeping the denominator unchanged.
Combining Constants: If there are constants outside the fraction that are being multiplied with the fraction, you can multiply these constants directly with the numerator.
Simplification: Always look for opportunities to simplify the expression by combining like terms or reducing fractions if possible.
Rearranging Terms: In algebra, it is common to write expressions with constants before variables (e.g., $20x$ instead of $x20$). This is more of a convention than a rule, but it helps with readability and standardization.
Maintaining the Order of Operations: Remember to follow the order of operations (PEMDAS/BODMAS) when simplifying expressions. Multiplication and division come before addition and subtraction, but any operation enclosed in parentheses should be done first.

In this problem, we did not have to use any advanced algebraic techniques such as factoring or expanding because the expression was already in a form that could be simplified through basic multiplication.