What is (3(2x-1)^2-(3x+5)(2x-1))/((2x-1)^4) ?

The solution to (3(2x-1)^2-(3x+5)(2x-1))/((2x-1)^4) is (3x-8)/((2x-1)^3)

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simplify (3(2x-1)^2-(3x+5)(2x-1))/((2x-1)^4)

simplify

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

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

Solution steps

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

Factor

3 (2 x - 1)^{2} - (3 x + 5) (2 x - 1) : (2 x - 1) (3 x - 8)

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(2 x - 1)^{4} = (2 x - 1) (2 x - 1)^{3}

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

Cancel the common factor:

2 x - 1

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

\frac{- 4}{- 1}

(n - 1) (2 n - 2)

4 \cdot 1 0^{4}

(4 x + y)^{3}

16 x + x^{5}

What is (3(2x-1)^2-(3x+5)(2x-1))/((2x-1)^4) ?
The solution to (3(2x-1)^2-(3x+5)(2x-1))/((2x-1)^4) is (3x-8)/((2x-1)^3)