For the equation, determine the constants A and B that make the equation an identity.
-$$\frac { x } { ( x + 8 ) ( x - 8 ) } = \frac { A } { ( x + 8 ) } + \frac { B } { ( x - 8 ) }$$
A) $\mathrm { A } = \frac { 1 } { 2 } , \mathrm {~B} = \frac { 1 } { 2 }$
B) $\mathrm { A } = \frac { 1 } { 2 } , \mathrm {~B} = 1$
C) $A = 1 , B = \frac { 1 } { 2 }$
D) $\mathrm { A } = - \frac { 1 } { 2 } , \mathrm {~B} = \frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

The equation is an identity if and only if A = 1/2 and B = 1/2.

For the Equation, Determine the Constants a and B That x(x+8)(x−8)=A(x+8)+B(x−8)\frac { x } { ( x + 8 ) ( x - 8 ) } = \frac { A } { ( x + 8 ) } + \frac { B } { ( x - 8 ) }(x+8)(x−8)x​=(x+8)A​+(x−8)B​

For the Equation, Determine the Constants a and B That $\frac { x } { ( x + 8 ) ( x - 8 ) } = \frac { A } { ( x + 8 ) } + \frac { B } { ( x - 8 ) }$