SOLUTION: Perform the indicated operations. Give the answer in lowest terms. {4}/{y^2-3y+2}+{6}/{y^2-1}

Algebra ->  Equations -> SOLUTION: Perform the indicated operations. Give the answer in lowest terms. {4}/{y^2-3y+2}+{6}/{y^2-1}       Log On


   

Question 201073: Perform the indicated operations. Give the answer in lowest terms.
{4}/{y^2-3y+2}+{6}/{y^2-1}

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
In order to add fractions, as you probably know, the denominators must be the same. And, as usual, it is advantageous to find and use the lowest common denominator (LCD).

When the denominators are polynomials, like your problem, the easiest way to find the LCD and to make each denominator equal to the LCD is to:
  1. Factor each denominator, as completely as possible.
  2. The LCD is the product of all the different factors in all the denominators. (If a factor appears in more than one denominator, use the highest exponent on this factor. For example, if %28x%2B9%29 is a factor of one denominator and %28x%2B9%29%5E2 is in another denominator, use %28x%2B9%29%5E2 in the LCD.)
  3. Multiply each the numerator and denominator of each fraction by the factors of the LCD it is "missing", if any.

Lets do this with your expression:
4%2F%28y%5E2+-3y+%2B2%29%2B6%2F%28y%5E2-1%29
1. Factor the denominators:
4%2F%28%28y+-+2%29%2A%28y+-+1%29%29%2B6%2F%28%28y%2B1%29+%2A+%28y+-+1%29%29
2. The LCD is the product of all the different factors in all the denominators:
LCD=%28y+-+2%29+%2A+%28y+-+1%29+%2A+%28y+%2B+1%29
3. Multiply each numerator and denominator of each fraction my any "missing" factors of the LCD. The first fraction is "missing" (y+1) and the second fraction is "missing" (y-2):

To continue we first multiply the numerators. (Leave the denominators factored.)

Next, add
%2810y-8%29%2F%28%28y-2%29%2A%28y-1%29%2A%28y%2B1%29%29
Next, factor the numerator to see if we can cancel common factors. (This is why we left the denominators factored earlier.). In this fraction, however, the numerator can only be factored into 2(5y-4) and so there are no common factors between the numerator and denominator to cancel. So the answer is
%2810y-8%29%2F%28%28y-2%29%2A%28y-1%29%2A%28y%2B1%29%29
Multiply the factors of the denominator in order to put this in simplified form.