What would the simplified equation be?

Question

(7x+3)/(x^2-7x+12) + (5)/(x-3)

ps The parantheses are just supposed to show seperation so it doesn't look confusing.

Answer 1

Hi Youssef,

 

What would the simplified equation be?
(7x+3)/(x^2-7x+12) + (5)/(x-3)
ps The parentheses are just supposed to show separation so it doesn't look confusing.

 

 

Youssef, parentheses are very important because of order of operations.

 

Looking at your problem the trinomial x²-7x+12 needs to be factored

x²-7x+12

(x-3)(x-4)

 

(7x+3)/(x^2-7x+12) + (5)/(x-3)

 

 

7x+3       +    5  

---------     -------

x²-7x+12     x-3

 

 

7x+3          +      5
-----------        -------
(x-3)(x-4)          x-3

 

 

The common denominator is (x-3)(x-4)

so you need to multipy the numerator of the 2nd term by (x-4)

 

 

7x+3 + 5(x-4)
----------------
(x-3)(x-4)

 

now  distribute and simplify

 

7x+3 + 5x-20
----------------
(x-3)(x-4)

 

 

12x-17
------------    is the answer
(x-3)(x-4)