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Preform the indicated operation. Simplify if possible

Preform the indicated operation. Simplify if possible 
 
    3     -    7  
x^2-4     x+2

3 Answers by Expert Tutors

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Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
0
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
Meena S. | Patient & knowledgeable Mathematics & Statistics (SPSS) TutorPatient & knowledgeable Mathematics & St...
4.5 4.5 (56 lesson ratings) (56)
0
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
 
 
Shelly J. | Excellent Maths Tutoring for academic successExcellent Maths Tutoring for academic su...
4.9 4.9 (217 lesson ratings) (217)
0
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.
 

Comments

Can you now simplify to A/(x-2) + B/(x+2) ?