Please simplify this

The answer is 4√3 - 6

Steps

(8√6mn + 6√8mn ) / 2√2mn

Factor out 2√mn from the expression

That's

2√mn × ( 4√6 - 3√8) / 2√2mn

Next reduce the fraction with 2

We have

√mn × ( 4√6 - 3√8) / √2mn

Factor √2 from the denominator

√mn × ( 4√6 - 3√8) / √2(√mn)

√mn will cancel each other

we get

( 4√6 - 3√8) / √2

Simplify the radical expression

That's

( 4√6 - 3× 2√2) / √2

= ( 4√6 - 6√2) / √2

Rationalize the surd

We get

( 4√6 - 6√2) / √2 × (√2 / √2)

= ( 4√6 - 6√2) (√2) / (√2)²

= 4√12 - 12 / 2

= (8 √3 - 12) / 2

Factor out 2 from the numerator

That's

2( 4 √ 3 - 6 ) /2

2 will cancel each other

so the final answer will be

4√3 - 6

Hope this helps you

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)