What is expand-((x-5)(2x+1))/((x-2)^2(x+3)) ?

The solution to expand-((x-5)(2x+1))/((x-2)^2(x+3)) is -(2x^2-9x-5)/(x^3-x^2-8x+12)

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expand-((x-5)(2x+1))/((x-2)^2(x+3))

expand

- \frac{( x - 5 ) ( 2 x + 1 )}{( x - 2 ) ^{2} ( x + 3 )}

- \frac{2 x ^{2} - 9 x - 5}{x ^{3} - x ^{2} - 8 x + 12}

Solution steps

- \frac{( x - 5 ) ( 2 x + 1 )}{( x - 2 ) ^{2} ( x + 3 )}

(x - 2)^{2} = x^{2} - 4 x + 4

= - \frac{( x - 5 ) ( 2 x + 1 )}{( x ^{2} - 4 x + 4 ) ( x + 3 )}

Expand

(x^{2} - 4 x + 4) (x + 3) : x^{3} - x^{2} - 8 x + 12

= - \frac{( x - 5 ) ( 2 x + 1 )}{x ^{3} - x ^{2} - 8 x + 12}

Expand

(x - 5) (2 x + 1) : 2 x^{2} - 9 x - 5

= - \frac{2 x ^{2} - 9 x - 5}{x ^{3} - x ^{2} - 8 x + 12}

- \frac{48 x}{( x ^{2} - 4 ) ^{2}}

(x + 3) (x - 3) (x - 4)

csc (x) (csc (x) + sin (x)) - c t an x (c t an x - tan (x))

5 x^{\frac{2}{3}} (8 x - 4 x^{\frac{1}{4}})

sec^{2} (5 x) + 3 (x - 1)^{2} - \frac{2}{3 x}

What is expand-((x-5)(2x+1))/((x-2)^2(x+3)) ?
The solution to expand-((x-5)(2x+1))/((x-2)^2(x+3)) is -(2x^2-9x-5)/(x^3-x^2-8x+12)