Partial Fractions
1 Decompose P/Q, Where Q Has Only Distinct Linear Factors
-$$\frac { 6 x + 5 } { x ^ { 2 } - 12 x + 35 }$$
A) $\frac { A } { x - 5 } + \frac { B } { x - 7 }$
B) $\frac { \mathrm { A } } { \mathrm { x } - 5 } + \frac { \mathrm { B } } { \mathrm { x } - 7 } + \frac { \mathrm { C } } { \mathrm { x } ^ { 2 } - 12 \mathrm { x } + 35 }$
C) $\frac { A } { x - 5 } + \frac { B } { x - 7 } + \frac { C x + D } { x ^ { 2 } - 12 x + 35 }$
D) $\frac { A } { x - 5 } + \frac { B } { x - 7 } + \frac { C } { ( x - 5 ) ^ { 2 } ( x - 7 ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

The denominator $x^2 - 12x + 35$ can be factored into $(x - 5)(x - 7)$, which are distinct linear factors. Therefore, the partial fraction decomposition involves terms of the form $\frac{A}{x - 5} + \frac{B}{x - 7}$, matching option A.

Partial Fractions 1 Decompose P/Q, Where Q Has Only Distinct 6x+5x2−12x+35\frac { 6 x + 5 } { x ^ { 2 } - 12 x + 35 }x2−12x+356x+5​

Partial Fractions
1 Decompose P/Q, Where Q Has Only Distinct $\frac { 6 x + 5 } { x ^ { 2 } - 12 x + 35 }$