Question

Which expression is equivalent to the expression below? (x/x+4)/x

Answer 1

Answer:

B) $\frac{\frac{x}{x+4}}{x}$ =  $\frac{x}{(x+4)}(\frac{1}{x})$

Step-by-step explanation:

Given : $\frac{\frac{x}{x+4}}{x}$.

To find : Which expression is equivalent to the expression below.

Solution : We have given that $\frac{\frac{x}{x+4}}{x}$.

By exponent rule  $(\frac{\frac{a}{b})}{c}$.

⇒  $\frac{a}{b} \cdot \frac{1}{c}$ =   $\frac{a}{bc}$.

Here a = x , b= x +4 , c =x.

Plugging the values

⇒  $\frac{x}{x +4} \xdot \frac{1}{c}$ =  $\frac{x}{x+4·x}$.

⇒   $\frac{x}{(x+4)} \cdot (\frac{1}{x})$.

Therefore,B) $\frac{\frac{x}{x+4}}{x}$ =  $\frac{x}{(x+4)}(\frac{1}{x})$

Answer 2

Answer:

Option b is correct.

the expression which is equivalent to the expression $\frac{\frac{x}{x+4}}{x}$ is,  $\frac{x}{(x+4)}(\frac{1}{x})$

Explanation:

Given: The expression is: $\frac{\frac{x}{x+4}}{x}$

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:  $(\frac{\frac{a}{b})}{c}$

⇒ $\frac{a}{b} \cdot \frac{1}{c}$

Now, we can easily get; $\frac{a \cdot 1}{b \cdot c}$ = $\frac{a}{bc}$

Let a = x , b = x+4 and c =x

then;

$\frac{(\frac{a}{b})}{c}$ = $\frac{a}{bc}$ = $\frac{x}{x \cdot (x+4)}$

or we can write it as $\frac{x}{(x+4)} \cdot (\frac{1}{x})$

Therefore, the expression which is equivalent to the expression $\frac{\frac{x}{x+4}}{x}$ is,  $\frac{x}{(x+4)}(\frac{1}{x})$