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

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

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simplify (-4(x^2-1)^2+4x*2(x^2-1)2x)/((x^2-1)^4)

simplify

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

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

Solution steps

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

Factor

- 4 (x^{2} - 1)^{2} + 4 x \cdot 2 (x^{2} - 1) \cdot 2 x : 4 (x + 1) (x - 1) (3 x^{2} + 1)

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

Factor

(x^{2} - 1)^{4} : (x + 1)^{4} (x - 1)^{4}

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

Apply exponent rule:

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

(x + 1)^{4} = (x + 1) (x + 1)^{3}

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

Cancel the common factor:

x + 1

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

Apply exponent rule:

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

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

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

Cancel the common factor:

x - 1

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

15 n - 19 n

\frac{\frac{x - 3}{2} + \frac{1}{x}}{\frac{1}{x} - \frac{1}{x ^{2}}}

\frac{x ^{2} - 3 x - 10}{x ^{2} - 7 x + 10}

(x^{2} - 5 x - 2) - (- 6 x^{2} - 7 x - 3)

- 3 a^{x + 1} + 2 a^{x + 1} - a^{x + 1} + 2 a^{x + 1}

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