Answer:
The expression equivalent to [tex]\frac{3x}{x+1}[/tex] ÷ [tex]x+1[/tex] is [tex]\frac{3x}{x+1}[/tex] × [tex]\frac{1}{x+1}[/tex] ⇒ 1st answer
Step-by-step explanation:
To divide two fraction we reciprocal the fraction after the division sign and change the division sign to multiplication sign
Ex : [tex]\frac{a}{b}[/tex] ÷ [tex]\frac{c}{d}[/tex] = [tex]\frac{a}{b}[/tex] × [tex]\frac{d}{c}[/tex]
∵ The expression is [tex]\frac{3x}{x+1}[/tex] ÷ [tex]x+1[/tex]
- Take the term after the division sign and reciprocal it
- Assume that the denominator of x + 1 is 1, then the numerator
of the reciprocal is 1 and the denominator is x + 1
∴ The reciprocal of [tex]x+1[/tex] is [tex]\frac{1}{x+1}[/tex]
- Change the division sign (÷) to multiplication sign (×)
∴ [tex]\frac{3x}{x+1}[/tex] ÷ [tex]x+1[/tex] = [tex]\frac{3x}{x+1}[/tex] × [tex]\frac{1}{x+1}[/tex]
The expression equivalent to [tex]\frac{3x}{x+1}[/tex] ÷ [tex]x+1[/tex] is [tex]\frac{3x}{x+1}[/tex] × [tex]\frac{1}{x+1}[/tex]
The expression that is equivalent to [tex]\frac{3x}{x + 1} \div x + 1[/tex] is: [tex]\mathbf{\frac{3x}{x + 1} \times \frac{1}{x + 1}}[/tex]
Given the expression, [tex]\frac{3x}{x + 1} \div x + 1[/tex], which is [tex]\frac{3x}{x + 1} \div \frac{x + 1}{1}[/tex],
To find the equivalent expression of [tex]\frac{3x}{x + 1} \div \frac{x + 1}{1}[/tex], change the multiplication sign to division sign, and turn the second fraction upside down, such that 1 will be the numerator, and x + 1 will be the denominator.
[tex]\frac{3x}{x + 1} \div \frac{x + 1}{1} = \frac{3x}{x + 1} \times \frac{1}{x + 1}[/tex]
Therefore, the expression that is equivalent to [tex]\frac{3x}{x + 1} \div x + 1[/tex] is: [tex]\mathbf{\frac{3x}{x + 1} \times \frac{1}{x + 1}}[/tex]
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