What is expand k/(x^2(3x+4)(x^2-x+6)^2) ?

The solution to expand k/(x^2(3x+4)(x^2-x+6)^2) is k/(3x^7-2x^6+31x^5+16x^4+60x^3+144x^2)

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expand k/(x^2(3x+4)(x^2-x+6)^2)

expand

\frac{k}{x ^{2} ( 3 x + 4 ) ( x ^{2} - x + 6 ) ^{2}}

\frac{k}{3 x ^{7} - 2 x ^{6} + 31 x ^{5} + 16 x ^{4} + 60 x ^{3} + 144 x ^{2}}

Solution steps

\frac{k}{x ^{2} ( 3 x + 4 ) ( x ^{2} - x + 6 ) ^{2}}

(x^{2} - x + 6)^{2} = x^{4} - 2 x^{3} + 13 x^{2} - 12 x + 36

= \frac{k}{x ^{2} ( 3 x + 4 ) ( x ^{4} - 2 x ^{3} + 13 x ^{2} - 12 x + 36 )}

Expand

x^{2} (3 x + 4) (x^{4} - 2 x^{3} + 13 x^{2} - 12 x + 36) : 3 x^{7} - 2 x^{6} + 31 x^{5} + 16 x^{4} + 60 x^{3} + 144 x^{2}

= \frac{k}{3 x ^{7} - 2 x ^{6} + 31 x ^{5} + 16 x ^{4} + 60 x ^{3} + 144 x ^{2}}

(cos (x) - cos (5 x)) sec (2 x)

6 x^{2} + 3 x \cdot (9 x^{2} - 8 x + 8)

\frac{x ( x - 6 )}{( x - 3 ) ^{2}}

\frac{2 N + ( a N t + b t + c ) ^{2}}{N}

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

What is expand k/(x^2(3x+4)(x^2-x+6)^2) ?
The solution to expand k/(x^2(3x+4)(x^2-x+6)^2) is k/(3x^7-2x^6+31x^5+16x^4+60x^3+144x^2)