Solve 1/3+4/x-2=6

$$\frac { 1 } { 3 } + \frac { 4 } { x - 2 } = 6$$

Solve for x

$$x = \frac{46}{17} = 2\frac{12}{17} \approx 2.705882353$$

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 3,x-2.

$$3\left(x-2\right)\times \frac{1}{3}+3\times 4=18\left(x-2\right)$$

Use the distributive property to multiply 3 by x-2.

$$\left(3x-6\right)\times \frac{1}{3}+3\times 4=18\left(x-2\right)$$

Use the distributive property to multiply 3x-6 by \frac{1}{3}.

$$x-2+3\times 4=18\left(x-2\right)$$

Multiply 3 and 4 to get 12.

$$x-2+12=18\left(x-2\right)$$

Add -2 and 12 to get 10.

$$x+10=18\left(x-2\right)$$

Use the distributive property to multiply 18 by x-2.

$$x+10=18x-36$$

Subtract 18x from both sides.

$$x+10-18x=-36$$

Combine x and -18x to get -17x.

$$-17x+10=-36$$

Subtract 10 from both sides.

$$-17x=-36-10$$

Subtract 10 from -36 to get -46.

$$-17x=-46$$

Divide both sides by -17.

$$x=\frac{-46}{-17}$$

Fraction \frac{-46}{-17} can be simplified to \frac{46}{17} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{46}{17}$$