Solve BS=(0,04-x)^2/(0,05-x)^2

$$B S = \frac { ( 0,04 - x ) ^ { 2 } } { ( 0,05 - x ) ^ { 2 } }$$

Solve for B

$$\left\{\begin{matrix}B=\frac{16\times \left(\frac{25x-1}{20x-1}\right)^{2}}{25S}\text{, }&x\neq \frac{1}{20}\text{ and }S\neq 0\\B\in \mathrm{R}\text{, }&S=0\text{ and }x=\frac{1}{25}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(0,04-x\right)^{2}.

$$BS=\frac{0,0016-0,08x+x^{2}}{\left(0,05-x\right)^{2}}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(0,05-x\right)^{2}.

$$BS=\frac{0,0016-0,08x+x^{2}}{0,0025-0,1x+x^{2}}$$

The equation is in standard form.

$$SB=\frac{x^{2}-\frac{2x}{25}+0,0016}{x^{2}-\frac{x}{10}+0,0025}$$

Divide both sides by S.

$$\frac{SB}{S}=\frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}S}$$

Dividing by S undoes the multiplication by S.

$$B=\frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}S}$$

Divide \frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}} by S.

$$B=\frac{16\left(25x-1\right)^{2}}{25S\left(20x-1\right)^{2}}$$

Solve for S

$$\left\{\begin{matrix}S=\frac{16\times \left(\frac{25x-1}{20x-1}\right)^{2}}{25B}\text{, }&x\neq \frac{1}{20}\text{ and }B\neq 0\\S\in \mathrm{R}\text{, }&B=0\text{ and }x=\frac{1}{25}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(0,04-x\right)^{2}.

$$BS=\frac{0,0016-0,08x+x^{2}}{\left(0,05-x\right)^{2}}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(0,05-x\right)^{2}.

$$BS=\frac{0,0016-0,08x+x^{2}}{0,0025-0,1x+x^{2}}$$

The equation is in standard form.

$$BS=\frac{x^{2}-\frac{2x}{25}+0,0016}{x^{2}-\frac{x}{10}+0,0025}$$

Divide both sides by B.

$$\frac{BS}{B}=\frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}B}$$

Dividing by B undoes the multiplication by B.

$$S=\frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}B}$$

Divide \frac{16\left(25x-1\right)^{2}}{25\left(20x-1\right)^{2}} by B.

$$S=\frac{16\left(25x-1\right)^{2}}{25B\left(20x-1\right)^{2}}$$