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

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

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

simplify

\frac{4 x - x ^{3}}{4 - 4 x + x ^{2}}

- \frac{x ( 2 + x )}{x - 2}

Solution steps

\frac{4 x - x ^{3}}{4 - 4 x + x ^{2}}

Factor

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

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

Factor

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

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

x (2 + x) (2 - x) = - x (2 + x) (x - 2)

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

Apply exponent rule:

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

(x - 2)^{2} = (x - 2) (x - 2)

= \frac{- x ( 2 + x ) ( x - 2 )}{( x - 2 ) ( x - 2 )}

Cancel the common factor:

x - 2

= \frac{- x ( 2 + x )}{x - 2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{x ( 2 + x )}{x - 2}

10 e^{0}

5 i \times i \times (- 2) i

lo g_{10} (0.00001)

\frac{a}{a + b} + \frac{b}{a - b}

\frac{1}{5} \div 6

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