Solve x-1/7x-1=x-3/7x-26

$$\frac { x - 1 } { 7 x - 1 } = \frac { x - 3 } { 7 x - 26 }$$

Solve for x

$$x = \frac{23}{11} = 2\frac{1}{11} \approx 2.090909091$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values \frac{1}{7},\frac{26}{7} since division by zero is not defined. Multiply both sides of the equation by \left(7x-26\right)\left(7x-1\right), the least common multiple of 7x-1,7x-26.

$$\left(7x-26\right)\left(x-1\right)=\left(7x-1\right)\left(x-3\right)$$

Use the distributive property to multiply 7x-26 by x-1 and combine like terms.

$$7x^{2}-33x+26=\left(7x-1\right)\left(x-3\right)$$

Use the distributive property to multiply 7x-1 by x-3 and combine like terms.

$$7x^{2}-33x+26=7x^{2}-22x+3$$

Subtract 7x^{2} from both sides.

$$7x^{2}-33x+26-7x^{2}=-22x+3$$

Combine 7x^{2} and -7x^{2} to get 0.

$$-33x+26=-22x+3$$

Add 22x to both sides.

$$-33x+26+22x=3$$

Combine -33x and 22x to get -11x.

$$-11x+26=3$$

Subtract 26 from both sides.

$$-11x=3-26$$

Subtract 26 from 3 to get -23.

$$-11x=-23$$

Divide both sides by -11.

$$x=\frac{-23}{-11}$$

Fraction \frac{-23}{-11} can be simplified to \frac{23}{11} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{23}{11}$$