Find the partial fraction decomposition for the rational expression.
$\frac { 2 x ^ { 3 } - 7 x ^ { 2 } + 5 x - 3 } { x ^ { 2 } + x - 2 }$
A) $2 x - 9 + \frac { 19 } { x + 2 } - \frac { - 1 } { x - 1 }$
B) $2 x + 9 + \frac { - 13 } { x + 2 } + \frac { 7 } { x - 1 }$
C) $2 x + 5 + \frac { - 7 / 3 } { x + 2 } + \frac { 13 / 3 } { x - 1 }$
D) $2 x - 9 + \frac { - 5 / 3 } { x + 2 } + \frac { 1 / 3 } { x - 1 }$

Question

Quizplus · Accepted Answer

The given rational expression can be decomposed into partial fractions by first performing polynomial long division, if necessary, and then breaking down the quotient further into simpler fractions. The correct decomposition is $2 x - 9 + \frac { 19 } { x + 2 } - \frac { - 1 } { x - 1 }$, which matches option A. This involves dividing the numerator by the denominator and then expressing the remainder as a sum of fractions whose denominators are the factors of the original denominator.

Find the Partial Fraction Decomposition for the Rational Expression 2x3−7x2+5x−3x2+x−2\frac { 2 x ^ { 3 } - 7 x ^ { 2 } + 5 x - 3 } { x ^ { 2 } + x - 2 }x2+x−22x3−7x2+5x−3​

Find the Partial Fraction Decomposition for the Rational Expression $\frac { 2 x ^ { 3 } - 7 x ^ { 2 } + 5 x - 3 } { x ^ { 2 } + x - 2 }$