A/3x-1 + B/(3x-1)^2

asked by guest
on Oct 21, 2024 at 8:15 am



You asked:

Evaluate the expression: \(\frac{A}{3 x} - 1 + \frac{B}{{\left( 3 x - 1 \right)}^{2}}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{A}{3 x} - 1 + \frac{B}{{\left( 3 x - 1 \right)}^{2}} = \frac{A}{3 x} + \frac{B}{\left(3 x - 1\right)^{2}} - 1 \)

Expanded

\[\frac{A}{3 x} - 1 + \frac{B}{{\left( 3 x - 1 \right)}^{2}} = \frac{A}{3 x} + \frac{B}{9 x^{2} - 6 x + 1} - 1\]

Factored

\[\frac{A}{3 x} - 1 + \frac{B}{{\left( 3 x - 1 \right)}^{2}} = \frac{9 x^{2} A - 6 A x + A + 3 B x - 27 x^{3} + 18 x^{2} - 3 x}{3 x \left(3 x - 1\right)^{2}}\]

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