Solve 4/x-6-6/4x+9+5/x-6=0

$$\frac { 4 } { x - 6 } - \frac { 6 } { 4 x + 9 } + \frac { 5 } { x - 6 } = 0$$

Solve for x

$$x = -\frac{39}{10} = -3\frac{9}{10} = -3.9$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{9}{4},6 since division by zero is not defined. Multiply both sides of the equation by \left(x-6\right)\left(4x+9\right), the least common multiple of x-6,4x+9.

$$\left(4x+9\right)\times 4-\left(x-6\right)\times 6+\left(4x+9\right)\times 5=0$$

Use the distributive property to multiply 4x+9 by 4.

$$16x+36-\left(x-6\right)\times 6+\left(4x+9\right)\times 5=0$$

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

$$16x+36-\left(6x-36\right)+\left(4x+9\right)\times 5=0$$

To find the opposite of 6x-36, find the opposite of each term.

$$16x+36-6x+36+\left(4x+9\right)\times 5=0$$

Combine 16x and -6x to get 10x.

$$10x+36+36+\left(4x+9\right)\times 5=0$$

Add 36 and 36 to get 72.

$$10x+72+\left(4x+9\right)\times 5=0$$

Use the distributive property to multiply 4x+9 by 5.

$$10x+72+20x+45=0$$

Combine 10x and 20x to get 30x.

$$30x+72+45=0$$

Add 72 and 45 to get 117.

$$30x+117=0$$

Subtract 117 from both sides. Anything subtracted from zero gives its negation.

$$30x=-117$$

Divide both sides by 30.

$$x=\frac{-117}{30}$$

Reduce the fraction \frac{-117}{30} to lowest terms by extracting and canceling out 3.

$$x=-\frac{39}{10}$$