# Solve for x: #1+1/(1+(1/(1+1/x))##=4#?

##### 2 Answers

#### Explanation:

Move

Then, multiply both sides by the denominator

Move

Again, multiply by the denominator so you can cancel it out.

Solve for

To check if the answer is correct, substitute the

#### Explanation:

Note that provided an equation is non-zero, then taking the reciprocal of both sides results in an equation which holds if and only if the original equation holds.

So one method of addressing the given example goes as folows..

Given:

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

Subtract

#1/(1+(1/(1+1/x))) = 3#

Take the reciprocal of both sides to get:

#1+(1/(1+1/x)) = 1/3#

Subtract

#1/(1+1/x) = -2/3#

Take the reciprocal of both sides to get:

#1+1/x = -3/2#

Subtract

#1/x = -5/2#

Take the reciprocal of both sides to get:

#x = -2/5#

Since all of the above steps are reversible, this is the solution of the given equation.