Solve frac{2F_{1}}{A_{1}}=F_2^prime/A_{2/3}

$$\frac { 2 F _ { 1 } } { A _ { 1 } } = \frac { F _ { 2 } ^ { \prime } } { A _ { 2 } / 3 }$$

Solve for A_1

$$A_{1}\neq 0$$

$$F_{1}=0\text{ and }A_{2}\neq 0$$

Steps for Solving Linear Equation

Variable A_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by A_{1}.

$$2F_{1}=3A_{1}A_{2}^{-1}\times \frac{\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})A_{2}}{3}$$

Express 3\times \frac{\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})A_{2}}{3} as a single fraction.

$$2F_{1}=\frac{3\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})A_{2}}{3}A_{1}A_{2}^{-1}$$

Cancel out 3 and 3.

$$2F_{1}=\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})A_{2}A_{1}A_{2}^{-1}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})A_{2}A_{1}A_{2}^{-1}=2F_{1}$$

Reorder the terms.

$$\frac{1}{A_{2}}A_{1}A_{2}\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})=2F_{1}$$

Multiply both sides of the equation by A_{2}.

$$1A_{1}A_{2}\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})=2F_{1}A_{2}$$

Reorder the terms.

$$A_{1}A_{2}\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})=2A_{2}F_{1}$$

The equation is in standard form.

$$0=2A_{2}F_{1}$$

This is false for any A_{1}.

$$A_{1}\in$$

Solve for A_2

$$A_{2}\neq 0$$

$$F_{1}=0\text{ and }A_{1}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by A_{1}.

$$2F_{1}=3A_{1}A_{2}^{-1}\times \frac{\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})A_{2}}{3}$$

Express 3\times \frac{\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})A_{2}}{3} as a single fraction.

$$2F_{1}=\frac{3\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})A_{2}}{3}A_{1}A_{2}^{-1}$$

Cancel out 3 and 3.

$$2F_{1}=\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})A_{2}A_{1}A_{2}^{-1}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})A_{2}A_{1}A_{2}^{-1}=2F_{1}$$

Reorder the terms.

$$\frac{1}{A_{2}}A_{1}A_{2}\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})=2F_{1}$$

Variable A_{2} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by A_{2}.

$$1A_{1}A_{2}\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})=2F_{1}A_{2}$$

Subtract 2F_{1}A_{2} from both sides.

$$1A_{1}A_{2}\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})-2F_{1}A_{2}=0$$

Reorder the terms.

$$A_{1}A_{2}\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})-2A_{2}F_{1}=0$$

Combine all terms containing A_{2}.

$$\left(A_{1}\frac{\mathrm{d}}{\mathrm{d}x}(F_{2})-2F_{1}\right)A_{2}=0$$

The equation is in standard form.

$$\left(-2F_{1}\right)A_{2}=0$$

Divide 0 by -2F_{1}.

$$A_{2}=0$$

Variable A_{2} cannot be equal to 0.

$$A_{2}\in \emptyset$$