Need help simplifying these questions answer asap

Question

simplify

1)

 

n+3 / n²-5n+6  (+) 6 / n²-7n+12

 

2)

 

Y²-20 / y²-4  (+)  6 / n²-7n+12

 

 

thanks so much 

 

/ means over 

 

Answer 1

First, we want to factor where possible.

 

1)

 

((n + 3) / (n² - 5n + 6)) + (6 / (n² - 7n + 12) =

 

((n + 3) / (n - 2)(n - 3)) + (6 / (n - 4)(n - 3))

 

 

Next, we use the LCD.  The LCD is (n - 3)(n - 4)(n - 2) .

 

((n + 3)(n - 4) / (n - 3)(n - 4)(n - 2)) + (6(n - 2) / (n - 3)(n - 4)(n - 2))

 

 

Now that we have an expression with a common denominator, we can add numerators.

 

((n + 3)(n - 4) + 6(n - 2)) / ((n - 3)(n - 4)(n - 2)) =

 

(n² - n - 12 + 6n - 12) / ((n - 3)(n - 4)(n - 2)) =

 

(n² + 5n - 24) / ((n - 3)(n - 4)(n - 2)) =

 

((n + 8)(n - 3)) / ((n - 3)(n - 4)(n - 2))

 

 

(n - 3) cancel each other out. 

 

 

(n + 8) / ((n -4)(n - 2))

 

 

 

The next problem is the same as the first.