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

The solution to factor 3(x-6)^2+2(x-6)^4-3/((x-6)) is (2x^5-60x^4+723x^3-4374x^2+13284x-16203)/(x-6)

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factor 3(x-6)^2+2(x-6)^4-3/((x-6))

factor

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

\frac{2 x ^{5} - 60 x ^{4} + 723 x ^{3} - 4374 x ^{2} + 13284 x - 16203}{x - 6}

Solution steps

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

Convert element to fraction:

3 (x - 6)^{2} = \frac{3 ( x - 6 ) ^{2} ( x - 6 )}{x - 6}, 2 (x - 6)^{4} = \frac{2 ( x - 6 ) ^{4} ( x - 6 )}{x - 6}

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

Since the denominators are equal, combine the fractions:

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

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

- 3 + 3 (x - 6)^{2} (x - 6) + 2 (x - 6)^{4} (x - 6) = - 3 + 3 (x - 6)^{3} + 2 (x - 6)^{5}

= \frac{- 3 + 3 ( x - 6 ) ^{3} + 2 ( x - 6 ) ^{5}}{x - 6}

Expand

- 3 + 3 (x - 6)^{3} + 2 (x - 6)^{5} : 2 x^{5} - 60 x^{4} + 723 x^{3} - 4374 x^{2} + 13284 x - 16203

= \frac{2 x ^{5} - 60 x ^{4} + 723 x ^{3} - 4374 x ^{2} + 13284 x - 16203}{x - 6}

30 + 2 w < 46

3 - 4 f < 7

4 (x - 1) (x - 5) > 0

\frac{1}{16}

4 = 2 (x + 3)

What is factor 3(x-6)^2+2(x-6)^4-3/((x-6)) ?
The solution to factor 3(x-6)^2+2(x-6)^4-3/((x-6)) is (2x^5-60x^4+723x^3-4374x^2+13284x-16203)/(x-6)