Write the partial fraction decomposition of the rational expression.
-$$\frac { 7 x ^ { 2 } - 7 x + 3 } { ( x - 1 ) ^ { 3 } }$$
A) $\frac { 7 } { x - 1 } - \frac { 7 } { ( x - 1 ) ^ { 2 } } + \frac { 3 } { ( x - 1 ) ^ { 3 } }$
B) $\frac { 7 } { x - 1 } + \frac { x + 7 } { ( x - 1 ) ^ { 2 } } + \frac { x ^ { 2 } + 3 } { ( x - 1 ) ^ { 3 } }$
C) $\frac { 7 } { x - 1 } + \frac { 7 } { ( x - 1 ) ^ { 2 } }$
D) $\frac { 7 } { x - 1 } + \frac { 7 } { ( x - 1 ) ^ { 2 } } + \frac { 3 } { ( x - 1 ) ^ { 3 } }$

Question

Quizplus · Accepted Answer

The correct partial fraction decomposition of the given rational expression is $\frac { 7 } { x - 1 } + \frac { 7 } { ( x - 1 ) ^ { 2 } } + \frac { 3 } { ( x - 1 ) ^ { 3 } }$, which matches option D. This decomposition correctly represents the original expression when the denominators are the powers of (x - 1).

Write the Partial Fraction Decomposition of the Rational Expression 7x2−7x+3(x−1)3\frac { 7 x ^ { 2 } - 7 x + 3 } { ( x - 1 ) ^ { 3 } }(x−1)37x2−7x+3​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 7 x ^ { 2 } - 7 x + 3 } { ( x - 1 ) ^ { 3 } }$