Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $$\frac { x - 3 } { x ^ { 2 } + 7 x + 12 }$$
A) $\frac { 3 } { x + 3 } + \frac { 3 } { x + 4 } + \frac { 3 } { x + 3 }$
B) $\frac { 1 } { x + 3 } + \frac { 1 } { x + 4 }$
C) $\frac { A } { x + 3 } - \frac { B } { x + 4 } + \frac { C } { x + 3 }$
D) $\frac { A } { x - 3 } - \frac { B } { x - 4 } + \frac { C } { x - 4 }$
E) $\frac { A } { x + 3 } + \frac { B } { x + 4 }$

Question

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ $$\frac { x - 3 } { x ^ { 2 } + 7 x + 12 }$$ ​
A) $\frac { 3 } { x + 3 } + \frac { 3 } { x + 4 } + \frac { 3 } { x + 3 }$
B) $\frac { 1 } { x + 3 } + \frac { 1 } { x + 4 }$
C) $\frac { A } { x + 3 } - \frac { B } { x + 4 } + \frac { C } { x + 3 }$
D) $\frac { A } { x - 3 } - \frac { B } { x - 4 } + \frac { C } { x - 4 }$
E) $\frac { A } { x + 3 } + \frac { B } { x + 4 }$

Quizplus · Accepted Answer

The denominator $x^2 + 7x + 12$ can be factored into $(x + 3)(x + 4)$. The correct form of partial fraction decomposition for a rational expression with distinct linear factors in the denominator is a sum of fractions, each with a constant numerator (represented by letters like A, B, etc.) and the linear factors of the denominator as the denominators. Therefore, the correct form is $\frac { A } { x + 3 } + \frac { B } { x + 4 }$.

Write the Form of the Partial Fraction Decomposition of the Rational