Solve 4/x^2-36-5/x^2-6x-3/x^2-6x=0

$$\frac { 4 } { x ^ { 2 } - 36 } - \frac { 5 } { x ^ { 2 } - 6 x } - \frac { 3 } { x ^ { 2 } - 6 x } = 0$$

Solve for x

$$x=-12$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -6,0,6 since division by zero is not defined. Multiply both sides of the equation by x\left(x-6\right)\left(x+6\right), the least common multiple of x^{2}-36,x^{2}-6x.

$$x\times 4-\left(x+6\right)\times 5-\left(x+6\right)\times 3=0$$

Use the distributive property to multiply x+6 by 5.

$$x\times 4-\left(5x+30\right)-\left(x+6\right)\times 3=0$$

To find the opposite of 5x+30, find the opposite of each term.

$$x\times 4-5x-30-\left(x+6\right)\times 3=0$$

Combine x\times 4 and -5x to get -x.

$$-x-30-\left(x+6\right)\times 3=0$$

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

$$-x-30-\left(3x+18\right)=0$$

To find the opposite of 3x+18, find the opposite of each term.

$$-x-30-3x-18=0$$

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

$$-4x-30-18=0$$

Subtract 18 from -30 to get -48.

$$-4x-48=0$$

Add 48 to both sides. Anything plus zero gives itself.

$$-4x=48$$

Divide both sides by -4.

$$x=\frac{48}{-4}$$

Divide 48 by -4 to get -12.

$$x=-12$$