What is 1/(x-1)-(3x-k)/(x^3-3x+2) ?

The solution to 1/(x-1)-(3x-k)/(x^3-3x+2) is (x^2-2x+k-2)/((x-1)^2(x+2))

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simplify 1/(x-1)-(3x-k)/(x^3-3x+2)

simplify

\frac{1}{x - 1} - \frac{3 x - k}{x ^{3} - 3 x + 2}

\frac{x ^{2} - 2 x + k - 2}{( x - 1 ) ^{2} ( x + 2 )}

Solution steps

\frac{1}{x - 1} - \frac{3 x - k}{x ^{3} - 3 x + 2}

Least Common Multiplier of

x - 1, x^{3} - 3 x + 2 : (x - 1)^{2} (x + 2)

Adjust Fractions based on the LCM

= \frac{( x - 1 ) ( x + 2 )}{( x - 1 ) ^{2} ( x + 2 )} - \frac{3 x - k}{( x - 1 ) ^{2} ( x + 2 )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{( x - 1 ) ( x + 2 ) - ( 3 x - k )}{( x - 1 ) ^{2} ( x + 2 )}

Simplify

(x - 1) (x + 2) - (3 x - k) : x^{2} - 2 x + k - 2

= \frac{x ^{2} - 2 x + k - 2}{( x - 1 ) ^{2} ( x + 2 )}

(- 5 + 3 i) \cdot (1 - 2 i)

\frac{\frac{x ^{3} - x}{x + 1}}{\frac{x - 1}{x + 1}}

\frac{cos ( θ )}{cot ( θ )}

2 sin (t) cos (t)

\frac{\frac{9 - x ^{2}}{3 x}}{\frac{x ^{2} + 6 x + 9}{3 x}}

What is 1/(x-1)-(3x-k)/(x^3-3x+2) ?
The solution to 1/(x-1)-(3x-k)/(x^3-3x+2) is (x^2-2x+k-2)/((x-1)^2(x+2))