What is factor 5t(6t+4)^{(-1)/2}+6(6t+4)^{1/2} ?

The solution to factor 5t(6t+4)^{(-1)/2}+6(6t+4)^{1/2} is (41t+24)/(2^{1/2)(3t+2)^{1/2}}

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factor 5t(6t+4)^{(-1)/2}+6(6t+4)^{1/2}

factor

5 t (6 t + 4)^{\frac{- 1}{2}} + 6 (6 t + 4)^{\frac{1}{2}}

\frac{41 t + 24}{2 ^{\frac{1}{2}} ( 3 t + 2 ) ^{\frac{1}{2}}}

Solution steps

5 t (6 t + 4)^{\frac{- 1}{2}} + 6 (6 t + 4)^{\frac{1}{2}}

Apply exponent rule:

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

(6 t + 4)^{\frac{1}{2}} = (6 t + 4)^{1 + \frac{- 1}{2}} = (6 t + 4)^{1} (6 t + 4)^{\frac{- 1}{2}}

= 5 t (6 t + 4)^{\frac{- 1}{2}} + 6 (6 t + 4)^{1} (6 t + 4)^{\frac{- 1}{2}}

Factor out common term

(4 + 6 t)^{\frac{- 1}{2}}

= (4 + 6 t)^{\frac{- 1}{2}} (5 t + 6 (4 + 6 t))

Factor

5 t + 6 (6 t + 4) : 41 t + 24

= (41 t + 24) (6 t + 4)^{\frac{- 1}{2}}

Refine

= \frac{41 t + 24}{( 6 t + 4 ) ^{\frac{1}{2}}}

(4 + 6 t)^{\frac{1}{2}} = (2 (3 t + 2))^{\frac{1}{2}}

= \frac{41 t + 24}{( 2 ( 3 t + 2 ) ) ^{\frac{1}{2}}}

(2 (3 t + 2))^{\frac{1}{2}} = 2^{\frac{1}{2}} (3 t + 2)^{\frac{1}{2}}

= \frac{41 t + 24}{2 ^{\frac{1}{2}} ( 3 t + 2 ) ^{\frac{1}{2}}}

\frac{- 6}{- 3}

0.22 m = 49.95 + 0.08 m

6 x^{2} - 3 x + 4 = 8 x + 1

4 x^{2} - 13 x - 12

2 x^{2} - 2 x + 1 = 0

What is factor 5t(6t+4)^{(-1)/2}+6(6t+4)^{1/2} ?
The solution to factor 5t(6t+4)^{(-1)/2}+6(6t+4)^{1/2} is (41t+24)/(2^{1/2)(3t+2)^{1/2}}