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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

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
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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 (57 lesson ratings) (57)
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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...
5.0 5.0 (256 lesson ratings) (256)
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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.