Solve 3/x+3+1/2(x-4)+6/(x-4)(x+3)=0

$$\frac { 3 } { x + 3 } + \frac { 1 } { 2 ( x - 4 ) } + \frac { 6 } { ( x - 4 ) ( x + 3 ) } = 0$$

Solve for x

$$x = \frac{9}{7} = 1\frac{2}{7} \approx 1.285714286$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,4 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-4\right)\left(x+3\right), the least common multiple of x+3,2\left(x-4\right),\left(x-4\right)\left(x+3\right).

$$\left(2x-8\right)\times 3+x+3+2\times 6=0$$

Use the distributive property to multiply 2x-8 by 3.

$$6x-24+x+3+2\times 6=0$$

Combine 6x and x to get 7x.

$$7x-24+3+2\times 6=0$$

Add -24 and 3 to get -21.

$$7x-21+2\times 6=0$$

Multiply 2 and 6 to get 12.

$$7x-21+12=0$$

Add -21 and 12 to get -9.

$$7x-9=0$$

Add 9 to both sides. Anything plus zero gives itself.

$$7x=9$$

Divide both sides by 7.

$$x=\frac{9}{7}$$