SOLUTION: {{{(a+b)/(a-b) - (a-b)/(a+b)}}}

Algebra ->  Rational-functions -> SOLUTION: {{{(a+b)/(a-b) - (a-b)/(a+b)}}}      Log On


   

Question 291137: %28a%2Bb%29%2F%28a-b%29+-+%28a-b%29%2F%28a%2Bb%29
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%2Bb%29%2F%28a-b%29+-+%28a-b%29%2F%28a%2Bb%29


Put parentheses around all binomials:

%28%28a%2Bb%29%29%2F%28%28a-b%29%29+-+%28%28a-b%29%29%2F%28%28a%2Bb%29%29

The LCD is red%28%28a-b%29%28a%2Bb%29%29

The first denominator %28a-b%29 needs red%28%28a%2Bb%29%29 to become the LCD
red%28%28a-b%29%28a%2Bb%29%29, so we multiply top and bottom of the first fraction
by red%28%28a%2Bb%29%29




The second denominator %28a%2Bb%29 needs red%28%28a-b%29%29 to become the LCD
red%28%28a-b%29%28a%2Bb%29%29, so we multiply top and bottom of the second fraction
by red%28%28a-b%29%29



The denominators are now the same, so we make just one fraction by
indicating the subtraction of the two numerators over the common
denominator:



FOIL out the binomials in the top and keep parentheses around them but DO NOT
FOIL out the binomial in the denominator!

%28%28a%5E2%2B2ab%2Bb%5E2%29+-+%28a%5E2-2ab%2Bb%5E2%29%29%2F%28%28a-b%29%28a%2Bb%29%29

Now remove the parentheses:

%28a%5E2%2B2ab%2Bb%5E2+-+a%5E2%2B2ab-b%5E2%29%2F%28%28a-b%29%28a%2Bb%29%29

Cancel the a%5E2 and the -a%5E2



Cancel the b%5E2 and the -b%5E2



%284ab%29%2F%28%28a-b%29%28a%2Bb%29%29

Edwin