Solve 661s=t^2+2/3-t^2

$$661s = \frac{ { t }^{ 2 } +2 }{ 3- { t }^{ 2 } }$$

Solve for s

$$s=\frac{t^{2}+2}{661\left(3-t^{2}\right)}$$

$$|t|\neq \sqrt{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -t^{2}+3.

$$661s\left(-t^{2}+3\right)=t^{2}+2$$

Use the distributive property to multiply 661s by -t^{2}+3.

$$-661st^{2}+1983s=t^{2}+2$$

Combine all terms containing s.

$$\left(-661t^{2}+1983\right)s=t^{2}+2$$

The equation is in standard form.

$$\left(1983-661t^{2}\right)s=t^{2}+2$$

Divide both sides by -661t^{2}+1983.

$$\frac{\left(1983-661t^{2}\right)s}{1983-661t^{2}}=\frac{t^{2}+2}{1983-661t^{2}}$$

Dividing by -661t^{2}+1983 undoes the multiplication by -661t^{2}+1983.

$$s=\frac{t^{2}+2}{1983-661t^{2}}$$

Divide t^{2}+2 by -661t^{2}+1983.

$$s=\frac{t^{2}+2}{661\left(3-t^{2}\right)}$$

Solve for t

$$t=\sqrt{\frac{1983s-2}{661s+1}}$$

$$t=-\sqrt{\frac{1983s-2}{661s+1}}\text{, }s\geq \frac{2}{1983}\text{ or }s<-\frac{1}{661}$$