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How to rewrite an expression with negative exponents such as :

-12(3x-1)^-5 *(6x+7)^5 + 30(3x-1)^-4 *(6x+7)^4

common factor is 6 but what can I pull out from the (3x-1)^-5 and (3x-1)^-4 ?

1 answer

( 3 x - 1 ) ^ -5 = 1 / ( 3 x -1 ) ^ 5

( 3x - 1 ) ^ - 4 = 1 / ( 3 x -1 ) ^ 4

- 12 ( 3 x -1 ) ^ - 5 * ( 6 x + 7 ) ^ 5 + 30 ( 3 x - 1 ) ^ - 4 * ( 6 x + 7) ^ 4 =

[ - 12 ( 6 x + 7 ) ^ 5 ) + 30 * ( 3 x - 1 ) * ( 6 x + 7 ) ^ 4 ] / ( 3 x - 1 ) ^ 5 =

6 * ( 6 x + 7 ) ^ 4 * [ ( - 2 ) * ( 6 x + 7 ) + 5 * ( 3 x - 1 ) ] / ( 3 x - 1 ) ^ 5 =

6 * ( 6 x + 7 ) ^ 4 * ( - 12 x - 14 + 15 x - 5 ) / ( 3 x - 1 ) ^ 5 =

6 * ( 6 x + 7 ) ^ 4 * ( 3 x - 19 ) / ( 3 x - 1 ) ^ 5
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