Solve 3/x-2-2/3=5

$$\frac { 3 } { x - 2 } - \frac { 2 } { 3 } = 5$$

Solve for x

$$x = \frac{43}{17} = 2\frac{9}{17} \approx 2.529411765$$

Steps for Solving Linear Equation

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-2\right), the least common multiple of x-2,3.

$$3\times 3+3\left(x-2\right)\left(-\frac{2}{3}\right)=15\left(x-2\right)$$

Multiply 3 and 3 to get 9.

$$9+3\left(x-2\right)\left(-\frac{2}{3}\right)=15\left(x-2\right)$$

Multiply 3 and -\frac{2}{3} to get -2.

$$9-2\left(x-2\right)=15\left(x-2\right)$$

Use the distributive property to multiply -2 by x-2.

$$9-2x+4=15\left(x-2\right)$$

Add 9 and 4 to get 13.

$$13-2x=15\left(x-2\right)$$

Use the distributive property to multiply 15 by x-2.

$$13-2x=15x-30$$

Subtract 15x from both sides.

$$13-2x-15x=-30$$

Combine -2x and -15x to get -17x.

$$13-17x=-30$$

Subtract 13 from both sides.

$$-17x=-30-13$$

Subtract 13 from -30 to get -43.

$$-17x=-43$$

Divide both sides by -17.

$$x=\frac{-43}{-17}$$

Fraction \frac{-43}{-17} can be simplified to \frac{43}{17} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{43}{17}$$