Solve 3/x-1+8/3=3

$$\frac { 3 } { x - 1 } + \frac { 8 } { 3 } = 3$$

Solve for x

$$x=10$$

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 3\left(x-1\right), the least common multiple of x-1,3.

$$3\times 3+3\left(x-1\right)\times \frac{8}{3}=9\left(x-1\right)$$

Multiply 3 and 3 to get 9.

$$9+3\left(x-1\right)\times \frac{8}{3}=9\left(x-1\right)$$

Multiply 3 and \frac{8}{3} to get 8.

$$9+8\left(x-1\right)=9\left(x-1\right)$$

Use the distributive property to multiply 8 by x-1.

$$9+8x-8=9\left(x-1\right)$$

Subtract 8 from 9 to get 1.

$$1+8x=9\left(x-1\right)$$

Use the distributive property to multiply 9 by x-1.

$$1+8x=9x-9$$

Subtract 9x from both sides.

$$1+8x-9x=-9$$

Combine 8x and -9x to get -x.

$$1-x=-9$$

Subtract 1 from both sides.

$$-x=-9-1$$

Subtract 1 from -9 to get -10.

$$-x=-10$$

Multiply both sides by -1.

$$x=10$$