(x+5) with exponent 1/2 equals (5-2x) with exponent 1/4

x = -2.

Step-by-step explanation:

(x + 5)^1/2 = (5 - 2x)^1/4

Taking both sides to the power of 4:

(x + 5)^2 = 5 - 2x

x^2 + 10x + 25 = 5 - 2x

x^2  + 12x + 20 = 0

(x + 10(x + 2) = 0

x = -2, -10

Test for extraneous roots.

When x = -10

(-10 + 5)^1/2 = (-5)^1/2 which is not real.

When x = -2

(-2+5)^1/2 = 3 ^1/2

(5 - 2*(-2)) ^1/4 = 9 ^ 1/4 = 3^1/2

so x = -2 is a root.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)