Question

The prime factorizations of the denominators of and are given below: 14p = 2(7)(p) 8p2 = 2(2)(2)(p)(p) Identify the LCD of and . LCD = What is each expression multiplied by to create an equivalent rational expression containing the common denominator? ( ) = ( ) =

Answer 1

1. C - 2(2)(2)(7)(p)(p)

2. B - 4p/4p

3. C - 7/7

Step-by-step explanation:

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Answer 2

`LCD = 56p^2`

`Expression = 4p` --- for 14p

`Expression =7` ------ for 8p²

Step-by-step explanation:

Given

`14p = 2(7)(p)`

`8p^2 = 2(2)(2)(p)(p)`

Required

Determine the LCD

To determine the LCD, we list out the union of the factors:

i.e.

`LCD = 2 * 7 * 2 * 2 * p * p`

`LCD = 56 * p^2`

`LCD = 56p^2`

To solve the (b) part;

Divide each the LCD by each expression

For 14p;

We have:

`Expression = (56p^2)/(14p)`

`Expression = (4 * 14 * p * p)/(14 * p)`

`Expression = 4 * p`

`Expression = 4p`

For 8p²

We have:

`Expression = (56p^2)/(8p^2)`

`Expression = (7 * 8 * p^2)/(8 * p^2)`

`Expression =7`