Express the following expressions in partial fractions: \(\frac{{{x}^{2}}+8x-1}{(x-3){{(x-1)}^{2}}}\

Question

Express the following expressions in partial fractions: $\frac{{{x}^{2}}+8x-1}{(x-3){{(x-1)}^{2}}}$ $\frac{{{x}^{2}}-x+1}{\left( 1-x \right){{(2x-1)}^{2}}}$ $\frac{1-2x+{{x}^{2}}}{\left( {{x}^{2}}-4 \right)(2x+3)}$

Accepted Answer

(a) $\frac{8}{x-3}-\frac{7}{x-1}-\frac{4}{(x-1)^2}$ (b) $\frac{1}{1-x}+\frac{3}{2(2x-1)}+\frac{3}{2(2x-1)^2}$ (c) $\frac{1}{28(x-2)}+\frac{9}{4(x+2)}-\frac{25}{7(2x+3)}$

Repeated Linear Factors in Denominator

Repeated Linear Factors in Denominator

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