Solve DOM=2x^2-3/(x^2-9)(x^2-4)

$$D O M = \frac { 2 x ^ { 2 } - 3 } { ( x ^ { 2 } - 9 ) ( x ^ { 2 } - 4 ) }$$

Solve for D (complex solution)

$$\left\{\begin{matrix}D=-\frac{3-2x^{2}}{MO\left(x^{4}-13x^{2}+36\right)}\text{, }&x\neq -2\text{ and }x\neq 2\text{ and }x\neq -3\text{ and }x\neq 3\text{ and }M\neq 0\text{ and }O\neq 0\\D\in \mathrm{C}\text{, }&\left(x=\frac{\sqrt{6}}{2}\text{ and }M=0\right)\text{ or }\left(x=-\frac{\sqrt{6}}{2}\text{ and }M=0\right)\text{ or }\left(x=-\frac{\sqrt{6}}{2}\text{ and }O=0\text{ and }M\neq 0\right)\text{ or }\left(x=\frac{\sqrt{6}}{2}\text{ and }O=0\text{ and }M\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-3\right)\left(x-2\right)\left(x+2\right)\left(x+3\right).

$$DOM\left(x-3\right)\left(x-2\right)\left(x+2\right)\left(x+3\right)=2x^{2}-3$$

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

$$\left(DOMx-3DOM\right)\left(x-2\right)\left(x+2\right)\left(x+3\right)=2x^{2}-3$$

Use the distributive property to multiply DOMx-3DOM by x-2 and combine like terms.

$$\left(DOMx^{2}-5DOMx+6DOM\right)\left(x+2\right)\left(x+3\right)=2x^{2}-3$$

Use the distributive property to multiply DOMx^{2}-5DOMx+6DOM by x+2 and combine like terms.

$$\left(DOMx^{3}-3DOMx^{2}-4xDOM+12DOM\right)\left(x+3\right)=2x^{2}-3$$

Use the distributive property to multiply DOMx^{3}-3DOMx^{2}-4xDOM+12DOM by x+3 and combine like terms.

$$DOMx^{4}-13x^{2}DOM+36DOM=2x^{2}-3$$

Combine all terms containing D.

$$\left(OMx^{4}-13x^{2}OM+36OM\right)D=2x^{2}-3$$

The equation is in standard form.

$$\left(MOx^{4}-13MOx^{2}+36MO\right)D=2x^{2}-3$$

Divide both sides by OMx^{4}-13MOx^{2}+36MO.

$$\frac{\left(MOx^{4}-13MOx^{2}+36MO\right)D}{MOx^{4}-13MOx^{2}+36MO}=\frac{2x^{2}-3}{MOx^{4}-13MOx^{2}+36MO}$$

Dividing by OMx^{4}-13MOx^{2}+36MO undoes the multiplication by OMx^{4}-13MOx^{2}+36MO.

$$D=\frac{2x^{2}-3}{MOx^{4}-13MOx^{2}+36MO}$$

Divide 2x^{2}-3 by OMx^{4}-13MOx^{2}+36MO.

$$D=\frac{2x^{2}-3}{MO\left(x^{4}-13x^{2}+36\right)}$$

Solve for M (complex solution)

$$\left\{\begin{matrix}M=-\frac{3-2x^{2}}{DO\left(x^{4}-13x^{2}+36\right)}\text{, }&x\neq -2\text{ and }x\neq 2\text{ and }x\neq -3\text{ and }x\neq 3\text{ and }O\neq 0\text{ and }D\neq 0\\M\in \mathrm{C}\text{, }&\left(x=\frac{\sqrt{6}}{2}\text{ and }O=0\right)\text{ or }\left(x=-\frac{\sqrt{6}}{2}\text{ and }O=0\right)\text{ or }\left(x=-\frac{\sqrt{6}}{2}\text{ and }D=0\text{ and }O\neq 0\right)\text{ or }\left(x=\frac{\sqrt{6}}{2}\text{ and }D=0\text{ and }O\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-3\right)\left(x-2\right)\left(x+2\right)\left(x+3\right).

$$DOM\left(x-3\right)\left(x-2\right)\left(x+2\right)\left(x+3\right)=2x^{2}-3$$

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

$$\left(DOMx-3DOM\right)\left(x-2\right)\left(x+2\right)\left(x+3\right)=2x^{2}-3$$

Use the distributive property to multiply DOMx-3DOM by x-2 and combine like terms.

$$\left(DOMx^{2}-5DOMx+6DMO\right)\left(x+2\right)\left(x+3\right)=2x^{2}-3$$

Use the distributive property to multiply DOMx^{2}-5DOMx+6DMO by x+2 and combine like terms.

$$\left(DOMx^{3}-3DOMx^{2}-4xDMO+12DOM\right)\left(x+3\right)=2x^{2}-3$$

Use the distributive property to multiply DOMx^{3}-3DOMx^{2}-4xDMO+12DOM by x+3 and combine like terms.

$$DOMx^{4}-13x^{2}DMO+36DMO=2x^{2}-3$$

Combine all terms containing M.

$$\left(DOx^{4}-13x^{2}DO+36DO\right)M=2x^{2}-3$$

The equation is in standard form.

$$\left(DOx^{4}-13DOx^{2}+36DO\right)M=2x^{2}-3$$

Divide both sides by -13ODx^{2}+36DO+DOx^{4}.

$$\frac{\left(DOx^{4}-13DOx^{2}+36DO\right)M}{DOx^{4}-13DOx^{2}+36DO}=\frac{2x^{2}-3}{DOx^{4}-13DOx^{2}+36DO}$$

Dividing by -13ODx^{2}+36DO+DOx^{4} undoes the multiplication by -13ODx^{2}+36DO+DOx^{4}.

$$M=\frac{2x^{2}-3}{DOx^{4}-13DOx^{2}+36DO}$$

Divide 2x^{2}-3 by -13ODx^{2}+36DO+DOx^{4}.

$$M=\frac{2x^{2}-3}{DO\left(x^{4}-13x^{2}+36\right)}$$

Solve for D

$$\left\{\begin{matrix}D=-\frac{3-2x^{2}}{MO\left(x^{4}-13x^{2}+36\right)}\text{, }&M\neq 0\text{ and }O\neq 0\text{ and }|x|\neq 2\text{ and }|x|\neq 3\\D\in \mathrm{R}\text{, }&\left(M=0\text{ or }O=0\right)\text{ and }|x|=\frac{\sqrt{6}}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-3\right)\left(x-2\right)\left(x+2\right)\left(x+3\right).

$$DOM\left(x-3\right)\left(x-2\right)\left(x+2\right)\left(x+3\right)=2x^{2}-3$$

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

$$\left(DOMx-3DOM\right)\left(x-2\right)\left(x+2\right)\left(x+3\right)=2x^{2}-3$$

Use the distributive property to multiply DOMx-3DOM by x-2 and combine like terms.

$$\left(DOMx^{2}-5DOMx+6DOM\right)\left(x+2\right)\left(x+3\right)=2x^{2}-3$$

Use the distributive property to multiply DOMx^{2}-5DOMx+6DOM by x+2 and combine like terms.

$$\left(DOMx^{3}-3DOMx^{2}-4xDOM+12DOM\right)\left(x+3\right)=2x^{2}-3$$

Use the distributive property to multiply DOMx^{3}-3DOMx^{2}-4xDOM+12DOM by x+3 and combine like terms.

$$DOMx^{4}-13x^{2}DOM+36DOM=2x^{2}-3$$

Combine all terms containing D.

$$\left(OMx^{4}-13x^{2}OM+36OM\right)D=2x^{2}-3$$

The equation is in standard form.

$$\left(MOx^{4}-13MOx^{2}+36MO\right)D=2x^{2}-3$$

Divide both sides by OMx^{4}-13MOx^{2}+36MO.

$$\frac{\left(MOx^{4}-13MOx^{2}+36MO\right)D}{MOx^{4}-13MOx^{2}+36MO}=\frac{2x^{2}-3}{MOx^{4}-13MOx^{2}+36MO}$$

Dividing by OMx^{4}-13MOx^{2}+36MO undoes the multiplication by OMx^{4}-13MOx^{2}+36MO.

$$D=\frac{2x^{2}-3}{MOx^{4}-13MOx^{2}+36MO}$$

Divide 2x^{2}-3 by OMx^{4}-13MOx^{2}+36MO.

$$D=\frac{2x^{2}-3}{MO\left(x^{4}-13x^{2}+36\right)}$$

Solve for M

$$\left\{\begin{matrix}M=-\frac{3-2x^{2}}{DO\left(x^{4}-13x^{2}+36\right)}\text{, }&O\neq 0\text{ and }D\neq 0\text{ and }|x|\neq 2\text{ and }|x|\neq 3\\M\in \mathrm{R}\text{, }&\left(O=0\text{ or }D=0\right)\text{ and }|x|=\frac{\sqrt{6}}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-3\right)\left(x-2\right)\left(x+2\right)\left(x+3\right).

$$DOM\left(x-3\right)\left(x-2\right)\left(x+2\right)\left(x+3\right)=2x^{2}-3$$

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

$$\left(DOMx-3DOM\right)\left(x-2\right)\left(x+2\right)\left(x+3\right)=2x^{2}-3$$

Use the distributive property to multiply DOMx-3DOM by x-2 and combine like terms.

$$\left(DOMx^{2}-5DOMx+6DMO\right)\left(x+2\right)\left(x+3\right)=2x^{2}-3$$

Use the distributive property to multiply DOMx^{2}-5DOMx+6DMO by x+2 and combine like terms.

$$\left(DOMx^{3}-3DOMx^{2}-4xDMO+12DOM\right)\left(x+3\right)=2x^{2}-3$$

Use the distributive property to multiply DOMx^{3}-3DOMx^{2}-4xDMO+12DOM by x+3 and combine like terms.

$$DOMx^{4}-13x^{2}DMO+36DMO=2x^{2}-3$$

Combine all terms containing M.

$$\left(DOx^{4}-13x^{2}DO+36DO\right)M=2x^{2}-3$$

The equation is in standard form.

$$\left(DOx^{4}-13DOx^{2}+36DO\right)M=2x^{2}-3$$

Divide both sides by -13ODx^{2}+36DO+DOx^{4}.

$$\frac{\left(DOx^{4}-13DOx^{2}+36DO\right)M}{DOx^{4}-13DOx^{2}+36DO}=\frac{2x^{2}-3}{DOx^{4}-13DOx^{2}+36DO}$$

Dividing by -13ODx^{2}+36DO+DOx^{4} undoes the multiplication by -13ODx^{2}+36DO+DOx^{4}.

$$M=\frac{2x^{2}-3}{DOx^{4}-13DOx^{2}+36DO}$$

Divide 2x^{2}-3 by -13ODx^{2}+36DO+DOx^{4}.

$$M=\frac{2x^{2}-3}{DO\left(x^{4}-13x^{2}+36\right)}$$