Question

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

a. (x/x+4)(x/1)
b. (x/x+4)(1/x)
c. (x+4/x)(1/x)
d. (x+4/x)(x/1)

Answer 1

B)
`((x)/(x+4))/(x)` =
`(x)/((x+4))((1)/(x))`

Step-by-step explanation:

Given :
`((x)/(x+4))/(x)`.

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

Solution : We have given that
`((x)/(x+4))/(x)`.

By exponent rule
`(((a)/(b)))/(c)`.

⇒
`(a)/(b) \cdot (1)/(c)` =
`(a)/(bc)`.

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

Plugging the values

⇒
`(x)/(x +4) \xdot (1)/(c)` =
`(x)/(x+4·x)`.

⇒
`(x)/((x+4)) \cdot ((1)/(x))`.

Therefore,B)
`((x)/(x+4))/(x)` =
`(x)/((x+4))((1)/(x))`

Answer 2

Option b is correct.

the expression which is equivalent to the expression
`((x)/(x+4))/(x)` is,
`(x)/((x+4))((1)/(x))`

Step-by-step explanation:

Given: The expression is:
`((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:
`(((a)/(b)))/(c)`

⇒
`(a)/(b) \cdot (1)/(c)`

Now, we can easily get;
`(a \cdot 1)/(b \cdot c)` =
`(a)/(bc)`

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

then;

`(((a)/(b)))/(c)` =
`(a)/(bc)` =
`(x)/(x \cdot (x+4))`

or we can write it as
`(x)/((x+4)) \cdot ((1)/(x))`

Therefore, the expression which is equivalent to the expression
`((x)/(x+4))/(x)` is,
`(x)/((x+4))((1)/(x))`