因式分解 2(5a-1)^{3/4}+7a(5a-1)^{-1/4}

解答

因式分解

2 (5 a - 1)^{\frac{3}{4}} + 7 a (5 a - 1)^{- \frac{1}{4}}

\frac{- 2 + 17 a}{( - 1 + 5 a ) ^{\frac{1}{4}}}

求解步骤

2 (5 a - 1)^{\frac{3}{4}} + 7 a (5 a - 1)^{- \frac{1}{4}}

使用指数法则:

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

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

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

因式分解出通项

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

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

乘开

7 a + 2 (5 a - 1) : - 2 + 17 a

= (17 a - 2) (5 a - 1)^{- \frac{1}{4}}

整理后得

= \frac{17 a - 2}{( 5 a - 1 ) ^{\frac{1}{4}}}

2 (- 5 x + 4) + 4 x - 5 = - 3

f a c t or 3 x^{2} - 20 x - 63

4 (2 x - 3) + 2 (x - 4) = 10

2 x + 6 = 3 x + 9 - 3

s im pl i f y 274