Preform the indicated operation. Simplify if possible

Question

Preform the indicated operation. Simplify if possible 

 

    3     -    7  

x^2-4     x+2

Answer 1

f(x) = 3/(x^2-4) – 7/(x+2)

f(x) = 3/((x+2)(x-2)) – 7(x-2)/((x-2)(x+2))

f(x) = (3 – 7(x-2))/((x-2)(x+2)), x ≠ ±2

f(x) = (17–7x)/((x-2)(x+2)), x ≠ ±2

Partial Fractions simplify further for use in calculus:

f(x) = (17–7x)/((x-2)(x+2)) = A/(x-2) + B/(x+2)

17–7x = A(x+2) + B(x–2) = (2A-2B) + (A+B)x

A + B = -7
2A-2B = 17
2A+2B =-14
4A = 3
A = 3/4
B = -A - 7 = -3/4 -28/4 = -31/4

f(x) = 3/(4(x-2)) – 31/(4(x+2)), x ≠ ±2

Answer 2

Hi Theresa,

 

factors of x^2-4= (x-2)(x+2)

 

     3                 -      7

__________           ____

(x-2)(x+2)             x+2

 

 

= 3- 7(x-2)

   _________

   (x-2)(x+2)

 

Ans  =  17-7x

           _____ 

           x^2-4

 

Meena from Strongsville,OH

 

 

Answer 3

Hi Theresa,

 

3/(x²-4) - 7/(x+2)

 

x²-4=(x)²-(2)²=(x-2)(x+2)

 

   3            -    7  

(x-2)(x+2)     (x+2)

 

3-7(x-2)

(x-2)(x+2)

 

3-7x+14

(x-2)(x+2)

 

  17-7x   

(x-2)(x+2)

 

For x=2 and -2 the solution is not defined.