Solve 10=x+1/x-5

$$10 = \frac { x + 1 } { x - 5 }$$

Solve for x

$$x = \frac{17}{3} = 5\frac{2}{3} \approx 5.666666667$$

Steps for Solving Linear Equation

Variable x cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by x-5.

$$10\left(x-5\right)=x+1$$

Use the distributive property to multiply 10 by x-5.

$$10x-50=x+1$$

Subtract x from both sides.

$$10x-50-x=1$$

Combine 10x and -x to get 9x.

$$9x-50=1$$

Add 50 to both sides.

$$9x=1+50$$

Add 1 and 50 to get 51.

$$9x=51$$

Divide both sides by 9.

$$x=\frac{51}{9}$$

Reduce the fraction \frac{51}{9} to lowest terms by extracting and canceling out 3.

$$x=\frac{17}{3}$$