What is factor 2x(x-5)^{-3}-4x^2(x-5)^{-4} ?

The solution to factor 2x(x-5)^{-3}-4x^2(x-5)^{-4} is (2x(-5-x))/((-5+x)^4)

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factor 2x(x-5)^{-3}-4x^2(x-5)^{-4}

factor

2 x (x - 5)^{- 3} - 4 x^{2} (x - 5)^{- 4}

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

Solution steps

2 x (x - 5)^{- 3} - 4 x^{2} (x - 5)^{- 4}

Apply exponent rule:

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

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

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

Rewrite as

= 2 x (- 5 + x)^{- 4} (- 5 + x) - 2 \cdot 2 x (- 5 + x)^{- 4} x

Factor out common term

2 x (- 5 + x)^{- 4}

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

Refine

= \frac{2 x ( - x - 5 )}{( x - 5 ) ^{4}}

8 n - (2 n - 3) = 12

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

5 - 3 x \geq 8 x - 7

- 0.25 x - 6 \leq - 3

15 = x - 14

What is factor 2x(x-5)^{-3}-4x^2(x-5)^{-4} ?
The solution to factor 2x(x-5)^{-3}-4x^2(x-5)^{-4} is (2x(-5-x))/((-5+x)^4)