Form of the Repeated Factors for a Partial Fraction

Algebra Level 1

When the following expression is expressed as a sum of partial fractions, what form will it take? x 3 − x + 1 x 4 − x 3 \frac{x^3-x+1}{x^4-x^3}

A x + B x 2 + C x 2 − x \frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^2-x} A x 3 + B x + 1 \frac{A}{x^3}+\frac{B}{x+1} A x + B x + C x + D x − 1 \frac{A}{x}+\frac{B}{x}+\frac{C}{x}+\frac{D}{x-1} A x + B x 2 + C x 3 + D x + 1 \frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{D}{x+1} A x + B x 2 + C x − 1 \frac{A}{x}+\frac{B}{x^2}+\frac{C}{x-1} A x + B x 2 + C x + 1 \frac{A}{x}+\frac{B}{x^2}+\frac{C}{x+1} A x 3 + B x 2 + C x \frac{A}{x^3}+\frac{B}{x^2}+\frac{C}{x} A x + B x 2 + C x 3 + D x − 1 \frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{D}{x-1}

Zane Gates by Zane Gates , 26, Australia

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1 solution

Zane Gates
Jun 7, 2019

Since the denominator of the expression factorizes as x 4 − x 3 = x 3 ( x − 1 ) x^4-x^3=x^3(x-1) , there will need to be terms with denominators x x , x 2 x^2 , x 3 x^3 and x − 1 x-1 .

7 Helpful 2 Interesting 0 Brilliant 3 Confused

is the answer A/x+B/x^2+C/x^3+D/x-1?

William Teder - 1 year, 2 months ago

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