Solve -3x+6/2x-4+x/x-2=-7/6

$$\frac { - 3 x + 6 } { 2 x - 4 } + \frac { x } { x - 2 } = - \frac { 7 } { 6 }$$

Solve for x

$$x=-1$$

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 6\left(x-2\right), the least common multiple of 2x-4,x-2,6.

$$3\left(-3x+6\right)+6x=-7\left(x-2\right)$$

Use the distributive property to multiply 3 by -3x+6.

$$-9x+18+6x=-7\left(x-2\right)$$

Combine -9x and 6x to get -3x.

$$-3x+18=-7\left(x-2\right)$$

Use the distributive property to multiply -7 by x-2.

$$-3x+18=-7x+14$$

Add 7x to both sides.

$$-3x+18+7x=14$$

Combine -3x and 7x to get 4x.

$$4x+18=14$$

Subtract 18 from both sides.

$$4x=14-18$$

Subtract 18 from 14 to get -4.

$$4x=-4$$

Divide both sides by 4.

$$x=\frac{-4}{4}$$

Divide -4 by 4 to get -1.

$$x=-1$$