Hi Angel;
Let's first take...
(x+5)/(x5)
Let's multiply this by (x+5)/(x+5)
[(x+5)/(x5)][(x+5)/(x+5)]
This is now...
(x+5)^{2}
(x5)(x+5)
Let's next take...
(x5)/(x+5)
and multiply this by (x5)/(x5)
[(x5)/(x+5)][(x5)/(x5)]
This is now...
(x5)^{2}
(x+5)(x5)
The result is...
[(x+5)^{2}][(x5)^{2}]
(x+5)(x5)
EXPANDED, THE NUMERATOR IS...
[(x+5)^{2}][(x5)^{2}]
(x^{2}+5x+5x+25)(x^{2}5x5x+25)
x^{2}x^{2} cancel.
(10x+25)(10x+25)
10x+25+10x25
20x
I WOULD BE DELIGHTED TO SETUP THE FOIL...
[(x+5)^{2}][(x5)^{2}]
As you already know, this is the numerator only.
[(x+5)(x+5)][(x5)(x5)]
Let's begin with the first bracketed equation...
(x+5)(x+5)
FOIL...
FIRST...(x)(x)=x^{2}
OUTER...(x)(5)=5x
INNER...(5)(x)=5x
LAST...(5)(5)=25
x^{2}+5x+5x+25
x^{2}+10x+25
The second bracketed equation...
(x5)(x5)
FOIL...
FIRST...(x)(x)=x^{2}
OUTER...(x)(5)=5x
INNER...(5)(x)=5x
LAST...(5)(5)=25
x^{2}5x5x+25
x^{2}10x+25
(x^{2}+10x+25)(x^{2}10x+25)
x^{2}x^{2} cancels
2525 cancels
10x(10x)
As you probably already know, subtracting a negative number is the same thing as adding a positive number...
10x+10x
20x
This is the result for the numerator you were looking for.
11/17/2013

Vivian L.
Comments