Solve 1/x=1/126+1/294+1/168

$$\frac{ 1 }{ x } = \frac{ 1 }{ 126 } + \frac{ 1 }{ 294 } + \frac{ 1 }{ 168 }$$

Solve for x

$$x = \frac{3528}{61} = 57\frac{51}{61} \approx 57.836065574$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3528x, the least common multiple of x,126,294,168.

$$3528=3528x\times \frac{1}{126}+3528x\times \frac{1}{294}+3528x\times \frac{1}{168}$$

Multiply 3528 and \frac{1}{126} to get \frac{3528}{126}.

$$3528=\frac{3528}{126}x+3528x\times \frac{1}{294}+3528x\times \frac{1}{168}$$

Divide 3528 by 126 to get 28.

$$3528=28x+3528x\times \frac{1}{294}+3528x\times \frac{1}{168}$$

Multiply 3528 and \frac{1}{294} to get \frac{3528}{294}.

$$3528=28x+\frac{3528}{294}x+3528x\times \frac{1}{168}$$

Divide 3528 by 294 to get 12.

$$3528=28x+12x+3528x\times \frac{1}{168}$$

Combine 28x and 12x to get 40x.

$$3528=40x+3528x\times \frac{1}{168}$$

Multiply 3528 and \frac{1}{168} to get \frac{3528}{168}.

$$3528=40x+\frac{3528}{168}x$$

Divide 3528 by 168 to get 21.

$$3528=40x+21x$$

Combine 40x and 21x to get 61x.

$$3528=61x$$

Swap sides so that all variable terms are on the left hand side.

$$61x=3528$$

Divide both sides by 61.

$$x=\frac{3528}{61}$$