What is factor 11x(2x-5)^{-1/4}-7(2x-5)^{3/4} ?

The solution to factor 11x(2x-5)^{-1/4}-7(2x-5)^{3/4} is -(3x-35)/((-5+2x)^{1/4)}

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factor 11x(2x-5)^{-1/4}-7(2x-5)^{3/4}

factor

11 x (2 x - 5)^{- \frac{1}{4}} - 7 (2 x - 5)^{\frac{3}{4}}

- \frac{3 x - 35}{( - 5 + 2 x ) ^{\frac{1}{4}}}

Solution steps

11 x (2 x - 5)^{- \frac{1}{4}} - 7 (2 x - 5)^{\frac{3}{4}}

Apply exponent rule:

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

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

= 11 x (2 x - 5)^{- \frac{1}{4}} - 7 (2 x - 5)^{1} (2 x - 5)^{- \frac{1}{4}}

Factor out common term

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

= (- 5 + 2 x)^{- \frac{1}{4}} (11 x - 7 (- 5 + 2 x))

Factor

11 x - 7 (2 x - 5) : - (3 x - 35)

= (- (3 x - 35)) (2 x - 5)^{- \frac{1}{4}}

Refine

= - \frac{3 x - 35}{( 2 x - 5 ) ^{\frac{1}{4}}}

9 x^{2} - 8 x

x^{2} + 10 x + 74 = 0

x + \frac{1}{5} x = 21

4 = - 3 x^{2} - 11 x

5 x - 5 > 15

What is factor 11x(2x-5)^{-1/4}-7(2x-5)^{3/4} ?
The solution to factor 11x(2x-5)^{-1/4}-7(2x-5)^{3/4} is -(3x-35)/((-5+2x)^{1/4)}