Quote (Ep0ch @ Jan 30 2018 09:44pm)

Where are you stuck exactly?

Quote (RzChaos @ Jan 31 2018 12:59am)

Remember that x ^ (-1) = 1/x

((6^-1+x^-1)^-1) = 4

(1/6 + 1/x) ^-1 = 4

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

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

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

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

6x = 4 * (x+6)

6x = 4x + 24

2x = 24

x = 12

Quote (RzChaos @ Jan 31 2018 02:39am)

Just fraction rules.

When you divide by a fraction, you multiply by the reciprocal.

For example...... (1/2) / (1/4) = (1/2)*(4/1)

Think of this the same way.

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

Quote (RzChaos @ Jan 31 2018 02:59am)

Remember that x ^ (-1) = 1/x

((6^-1+x^-1)^-1) = 4

(1/6 + 1/x) ^-1 = 4

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

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

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

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

6x = 4 * (x+6)

6x = 4x + 24

2x = 24

x = 12

Quote (Leevee @ Jan 31 2018 07:38am)

Alternatively

((6^-1+x^-1)^-1) = 4

Rewrite the left part so that ^-1 become fractions:
1/(1/6 + 1/x) = 4

Multiply both sides by (1/6 + 1/x):
1 = 4(1/6 + 1/x)

In the right side, use distribution to multiply both 1/6 and 1/x by 4:
1 = 4/6 + 4/x

Subtract 4/6 from both sides:
2/6 = 4/x

Simplify left side:
1/3 = 4/x

Divide both sides by 4:
1/12 = 1/x

Simplify:
12 = x

:)