Answer:
Problem: [tex]\frac{x-8}{x+11} \cdot \frac{x+8}{x-11}[/tex]
Answer: [tex]\frac{x^2-64}{x^2-121}[/tex]
Step-by-step explanation:
[tex]\frac{x-8}{x+11} \cdot \frac{x+8}{x-11}[/tex]
Writing as one fraction:
[tex]\frac{(x-8)(x+8)}{(x+11)(x-11)}[/tex]
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:
[tex](a-b)(a+b)=a^2-b^2[/tex].
So your problem becomes this after the multiplication of conjugates:
[tex]\frac{x^2-64}{x^2-121}[/tex]
Answer:
[tex] \frac { ( x - 8 ) ( x + 8 ) } { ( x + 1 1 ) ( x - 1 1 ) } [/tex]
Step-by-step explanation:
We are to find the product of the rational expression below:
[tex] \frac { x - 8 } { x + 1 1 } \times \frac { x + 8 } { x - 1 1 } [/tex]
We are to multiply these terms by taking the LCM to get:
[tex] \frac { ( x - 8 ) ( x + 8 ) } { ( x + 1 1 ) ( x - 1 1 ) } [/tex]
Since the signs of all the terms are different so we cannot add them up.
