Question

What is the product of the rational expressions below? x-8/x+11*x+8/x-11

Answer 1

`\frac { ( x - 8 ) ( x + 8 ) } { ( x + 1 1 ) ( x - 1 1 ) }`

Explanation:

We are to find the product of the rational expression below:

`\frac { x - 8 } { x + 1 1 } * \frac { x + 8 } { x - 1 1 }`

We are to multiply these terms by taking the LCM to get:

`\frac { ( x - 8 ) ( x + 8 ) } { ( x + 1 1 ) ( x - 1 1 ) }`

Since the signs of all the terms are different so we cannot add them up.

Answer 2

Problem:
`(x-8)/(x+11) \cdot (x+8)/(x-11)`

Answer:
`(x^2-64)/(x^2-121)`

Explanation:

`(x-8)/(x+11) \cdot (x+8)/(x-11)`

Writing as one fraction:

`((x-8)(x+8))/((x+11)(x-11))`

Now before we continue, notice both of your bottom and top are in the form of (a-b)(a+b) or (a+b)(a-b) which is the same format.

That is, we are multiplying conjugates on top and bottom.

When multiplying conjugates, all you have to do it first and last.

For example:

`(a-b)(a+b)=a^2-b^2`.

So your problem becomes this after the multiplication of conjugates:

`(x^2-64)/(x^2-121)`