Answer:
Option b is correct.
the expression which is equivalent to the expression [tex]\frac{\frac{x}{x+4}}{x}[/tex] is, [tex]\frac{x}{(x+4)}(\frac{1}{x})[/tex]
Explanation:
Given: The expression is: [tex]\frac{\frac{x}{x+4}}{x}[/tex]
We remember that dividing fraction a by fraction b is the same as multiplying fraction a by the reciprocal of fraction b or vice versa. Also any number can be expressed as itself over 1.
Using expression: [tex](\frac{\frac{a}{b})}{c}[/tex]
⇒ [tex]\frac{a}{b} \cdot \frac{1}{c}[/tex]
Now, we can easily get; [tex]\frac{a \cdot 1}{b \cdot c}[/tex] = [tex]\frac{a}{bc}[/tex]
Let a = x , b = x+4 and c =x
then;
[tex]\frac{(\frac{a}{b})}{c}[/tex] = [tex]\frac{a}{bc}[/tex] = [tex]\frac{x}{x \cdot (x+4)}[/tex]
or we can write it as [tex]\frac{x}{(x+4)} \cdot (\frac{1}{x})[/tex]
Therefore, the expression which is equivalent to the expression [tex]\frac{\frac{x}{x+4}}{x}[/tex] is, [tex]\frac{x}{(x+4)}(\frac{1}{x})[/tex]
Answer:
B) [tex]\frac{\frac{x}{x+4}}{x}[/tex] = [tex]\frac{x}{(x+4)}(\frac{1}{x})[/tex]
Step-by-step explanation:
Given : [tex]\frac{\frac{x}{x+4}}{x}[/tex].
To find : Which expression is equivalent to the expression below.
Solution : We have given that [tex]\frac{\frac{x}{x+4}}{x}[/tex].
By exponent rule [tex](\frac{\frac{a}{b})}{c}[/tex].
⇒ [tex]\frac{a}{b} \cdot \frac{1}{c}[/tex] = [tex]\frac{a}{bc}[/tex].
Here a = x , b= x +4 , c =x.
Plugging the values
⇒ [tex]\frac{x}{x +4} \xdot \frac{1}{c}[/tex] = [tex]\frac{x}{x+4·x}[/tex].
⇒ [tex]\frac{x}{(x+4)} \cdot (\frac{1}{x})[/tex].
Therefore,B) [tex]\frac{\frac{x}{x+4}}{x}[/tex] = [tex]\frac{x}{(x+4)}(\frac{1}{x})[/tex]
