Solve 1/x-1/7=1/10

$$\frac { 1 } { x } - \frac { 1 } { 7 } = \frac { 1 } { 10 }$$

Solve for x

$$x = \frac{70}{17} = 4\frac{2}{17} \approx 4.117647059$$

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 70x, the least common multiple of x,7,10.

$$70+70x\left(-\frac{1}{7}\right)=7x$$

Express 70\left(-\frac{1}{7}\right) as a single fraction.

$$70+\frac{70\left(-1\right)}{7}x=7x$$

Multiply 70 and -1 to get -70.

$$70+\frac{-70}{7}x=7x$$

Divide -70 by 7 to get -10.

$$70-10x=7x$$

Subtract 7x from both sides.

$$70-10x-7x=0$$

Combine -10x and -7x to get -17x.

$$70-17x=0$$

Subtract 70 from both sides. Anything subtracted from zero gives its negation.

$$-17x=-70$$

Divide both sides by -17.

$$x=\frac{-70}{-17}$$

Fraction \frac{-70}{-17} can be simplified to \frac{70}{17} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{70}{17}$$