Solve 1/x-1-2/7=3

$$\frac { 1 } { x - 1 } - \frac { 2 } { 7 } = 3$$

Solve for x

$$x = \frac{30}{23} = 1\frac{7}{23} \approx 1.304347826$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 7\left(x-1\right), the least common multiple of x-1,7.

$$7+7\left(x-1\right)\left(-\frac{2}{7}\right)=21\left(x-1\right)$$

Multiply 7 and -\frac{2}{7} to get -2.

$$7-2\left(x-1\right)=21\left(x-1\right)$$

Use the distributive property to multiply -2 by x-1.

$$7-2x+2=21\left(x-1\right)$$

Add 7 and 2 to get 9.

$$9-2x=21\left(x-1\right)$$

Use the distributive property to multiply 21 by x-1.

$$9-2x=21x-21$$

Subtract 21x from both sides.

$$9-2x-21x=-21$$

Combine -2x and -21x to get -23x.

$$9-23x=-21$$

Subtract 9 from both sides.

$$-23x=-21-9$$

Subtract 9 from -21 to get -30.

$$-23x=-30$$

Divide both sides by -23.

$$x=\frac{-30}{-23}$$

Fraction \frac{-30}{-23} can be simplified to \frac{30}{23} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{30}{23}$$