Solve 22y+1/y-1=31

$$\frac { 22 y + 1 } { y - 1 } = 31$$

Solve for y

$$y = \frac{32}{9} = 3\frac{5}{9} \approx 3.555555556$$

Steps for Solving Linear Equation

Variable y cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by y-1.

$$22y+1=31\left(y-1\right)$$

Use the distributive property to multiply 31 by y-1.

$$22y+1=31y-31$$

Subtract 31y from both sides.

$$22y+1-31y=-31$$

Combine 22y and -31y to get -9y.

$$-9y+1=-31$$

Subtract 1 from both sides.

$$-9y=-31-1$$

Subtract 1 from -31 to get -32.

$$-9y=-32$$

Divide both sides by -9.

$$y=\frac{-32}{-9}$$

Fraction \frac{-32}{-9} can be simplified to \frac{32}{9} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{32}{9}$$