Solve l/r=1+ecosθ

$$\frac { l } { r } = 1 + e \cos \theta$$

Solve for l

$$l=r\left(e\cos(\theta )+1\right)$$

$$r\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{1}{r}l=e\cos(\theta )+1$$

Divide both sides by r^{-1}.

$$\frac{\frac{1}{r}lr}{1}=\frac{\left(e\cos(\theta )+1\right)r}{1}$$

Dividing by r^{-1} undoes the multiplication by r^{-1}.

$$l=\frac{\left(e\cos(\theta )+1\right)r}{1}$$

Divide 1+e\cos(\theta ) by r^{-1}.

$$l=r\left(e\cos(\theta )+1\right)$$

Solve for r

$$\left\{\begin{matrix}r=\frac{l}{e\cos(\theta )+1}\text{, }&l\neq 0\text{ and }\nexists n_{2}\in \mathrm{Z}\text{ : }\theta =2\pi n_{2}+\arccos(\frac{1}{e})+\pi \text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =2\pi n_{1}-\arccos(\frac{1}{e})+\pi \\r\neq 0\text{, }&\left(\exists n_{4}\in \mathrm{Z}\text{ : }\theta =2\pi n_{4}+\arccos(\frac{1}{e})+\pi \text{ or }\exists n_{3}\in \mathrm{Z}\text{ : }\theta =2\pi n_{3}-\arccos(\frac{1}{e})+\pi \right)\text{ and }l=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$l=r+e\cos(\theta )r$$

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

$$r+e\cos(\theta )r=l$$

Combine all terms containing r.

$$\left(1+e\cos(\theta )\right)r=l$$

The equation is in standard form.

$$\left(e\cos(\theta )+1\right)r=l$$

Divide both sides by 1+e\cos(\theta ).

$$\frac{\left(e\cos(\theta )+1\right)r}{e\cos(\theta )+1}=\frac{l}{e\cos(\theta )+1}$$

Dividing by 1+e\cos(\theta ) undoes the multiplication by 1+e\cos(\theta ).

$$r=\frac{l}{e\cos(\theta )+1}$$

Variable r cannot be equal to 0.

$$r=\frac{l}{e\cos(\theta )+1}\text{, }r\neq 0$$