Solve (A+B)x^2=(a+d)+1

$$( A + B ) x ^ { 2 } = ( a + d ) + 1$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=\frac{1+d+a-Bx^{2}}{x^{2}}\text{, }&x\neq 0\\A\in \mathrm{C}\text{, }&a=-d-1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply A+B by x^{2}.

$$Ax^{2}+Bx^{2}=a+d+1$$

Subtract Bx^{2} from both sides.

$$Ax^{2}=a+d+1-Bx^{2}$$

Reorder the terms.

$$Ax^{2}=-Bx^{2}+a+d+1$$

The equation is in standard form.

$$x^{2}A=1+d+a-Bx^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}A}{x^{2}}=\frac{1+d+a-Bx^{2}}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$A=\frac{1+d+a-Bx^{2}}{x^{2}}$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=\frac{1+d+a-Ax^{2}}{x^{2}}\text{, }&x\neq 0\\B\in \mathrm{C}\text{, }&a=-d-1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply A+B by x^{2}.

$$Ax^{2}+Bx^{2}=a+d+1$$

Subtract Ax^{2} from both sides.

$$Bx^{2}=a+d+1-Ax^{2}$$

Reorder the terms.

$$Bx^{2}=-Ax^{2}+a+d+1$$

The equation is in standard form.

$$x^{2}B=1+d+a-Ax^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}B}{x^{2}}=\frac{1+d+a-Ax^{2}}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$B=\frac{1+d+a-Ax^{2}}{x^{2}}$$

Solve for A

$$\left\{\begin{matrix}A=\frac{1+d+a-Bx^{2}}{x^{2}}\text{, }&x\neq 0\\A\in \mathrm{R}\text{, }&a=-d-1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply A+B by x^{2}.

$$Ax^{2}+Bx^{2}=a+d+1$$

Subtract Bx^{2} from both sides.

$$Ax^{2}=a+d+1-Bx^{2}$$

Reorder the terms.

$$Ax^{2}=-Bx^{2}+a+d+1$$

The equation is in standard form.

$$x^{2}A=1+d+a-Bx^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}A}{x^{2}}=\frac{1+d+a-Bx^{2}}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$A=\frac{1+d+a-Bx^{2}}{x^{2}}$$

Solve for B

$$\left\{\begin{matrix}B=\frac{1+d+a-Ax^{2}}{x^{2}}\text{, }&x\neq 0\\B\in \mathrm{R}\text{, }&a=-d-1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply A+B by x^{2}.

$$Ax^{2}+Bx^{2}=a+d+1$$

Subtract Ax^{2} from both sides.

$$Bx^{2}=a+d+1-Ax^{2}$$

Reorder the terms.

$$Bx^{2}=-Ax^{2}+a+d+1$$

The equation is in standard form.

$$x^{2}B=1+d+a-Ax^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}B}{x^{2}}=\frac{1+d+a-Ax^{2}}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$B=\frac{1+d+a-Ax^{2}}{x^{2}}$$