Solve 1/x-1=1/7x

$$\frac{ 1 }{ x } -1 = \frac{ 1 }{ 7x }$$

Solve for x

$$x=\frac{6}{7}\approx 0.857142857$$

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 7x, the least common multiple of x,7x.

$$7+7x\left(-1\right)=1$$

Multiply 7 and -1 to get -7.

$$7-7x=1$$

Subtract 7 from both sides.

$$-7x=1-7$$

Subtract 7 from 1 to get -6.

$$-7x=-6$$

Divide both sides by -7.

$$x=\frac{-6}{-7}$$

Fraction \frac{-6}{-7} can be simplified to \frac{6}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{6}{7}$$