Find the partial fraction decomposition.
-$$\frac { 3 } { x ^ { 2 } + 4 x + 3 } = \frac { A } { x + 3 } + \frac { B } { x + 1 }$$
A) $A = - \frac { 3 } { 2 } , B = - \frac { 3 } { 2 }$
B) $A = \frac { 3 } { 2 } , B = \frac { 3 } { 2 }$
C) $\mathrm { A } = \frac { 3 } { 2 } , \mathrm {~B} = - \frac { 3 } { 2 }$
D) $\mathrm { A } = - \frac { 3 } { 2 } , \mathrm {~B} = \frac { 3 } { 2 }$

Question

Quizplus · Accepted Answer

The partial fraction decomposition requires solving for A and B such that $3 = A(x+1) + B(x+3)$. Solving this system gives $A = -\frac{3}{2}$ and $B = \frac{3}{2}$.

Find the Partial Fraction Decomposition 3x2+4x+3=Ax+3+Bx+1\frac { 3 } { x ^ { 2 } + 4 x + 3 } = \frac { A } { x + 3 } + \frac { B } { x + 1 }x2+4x+33​=x+3A​+x+1B​

Find the Partial Fraction Decomposition $\frac { 3 } { x ^ { 2 } + 4 x + 3 } = \frac { A } { x + 3 } + \frac { B } { x + 1 }$