Solve x+1/x-6=71

$$\frac { x + 1 } { x - 6 } = 71$$

Solve for x

$$x = \frac{61}{10} = 6\frac{1}{10} = 6.1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 6 since division by zero is not defined. Multiply both sides of the equation by x-6.

$$x+1=71\left(x-6\right)$$

Use the distributive property to multiply 71 by x-6.

$$x+1=71x-426$$

Subtract 71x from both sides.

$$x+1-71x=-426$$

Combine x and -71x to get -70x.

$$-70x+1=-426$$

Subtract 1 from both sides.

$$-70x=-426-1$$

Subtract 1 from -426 to get -427.

$$-70x=-427$$

Divide both sides by -70.

$$x=\frac{-427}{-70}$$

Reduce the fraction \frac{-427}{-70} to lowest terms by extracting and canceling out -7.

$$x=\frac{61}{10}$$