Respuesta :
Answer:
B
Step-by-step explanation:
Given
[tex]\frac{x-2}{x+3}[/tex] ÷ [tex]\frac{2}{x}[/tex]
Leave the first fraction, change division to multiplication and turn the second fraction upside down, that is
= [tex]\frac{x-2}{x+3}[/tex] × [tex]\frac{x}{2}[/tex]
= [tex]\frac{x(x-2)}{2(x+3)}[/tex]
= [tex]\frac{x^2-2x}{2x+6}[/tex] → B
The quotient of rational expressions [tex]\frac{x-2}{x+3}[/tex] divided by [tex]\frac{2}{x}[/tex] is [tex]\bold{\frac{x^{2} -2x}{2x+6}}[/tex] .
The correct answer is option (b).
What is rational expression?
"A rational expression is the ratio of two polynomials. "
What is quotient?
"The result of the division is the quotient."
For given example,
We need to find the quotient of rational expressions [tex]\frac{x-2}{x+3} \div \frac{2}{x}[/tex]
[tex]\frac{x-2}{x+3} \div \frac{2}{x} \\\\= \frac{\frac{x-2}{x+3}}{\frac{2}{x}} \\\\= \frac{x-2}{x+3} \times \frac{x}{2}\\\\= \frac{x\times (x-2)}{2\times (x+3)}\\ \\=\bold{\frac{x^{2} -2x}{2x+6}}[/tex]
Therefore, the quotient of [tex]\frac{x-2}{x+3}[/tex] divided by [tex]\frac{2}{x}[/tex] is [tex]\bold{\frac{x^{2} -2x}{2x+6}}[/tex] .
The correct answer is option (b).
Learn more about rational expressions here:
https://brainly.com/question/17134322
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