Solve 6.61s=t^2+2/3-t^2

$$6.61s = \frac{ { t }^{ 2 } +2 }{ 3- { t }^{ 2 } }$$

Solve for s

$$s=-\frac{100\left(t^{2}+2\right)}{661\left(t^{2}-3\right)}$$

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

Steps for Solving Linear Equation

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

$$6.61s\left(-t^{2}+3\right)=t^{2}+2$$

Use the distributive property to multiply 6.61s by -t^{2}+3.

$$-6.61st^{2}+19.83s=t^{2}+2$$

Combine all terms containing s.

$$\left(-6.61t^{2}+19.83\right)s=t^{2}+2$$

The equation is in standard form.

$$\frac{1983-661t^{2}}{100}s=t^{2}+2$$

Divide both sides by -6.61t^{2}+19.83.

$$\frac{100\times \frac{1983-661t^{2}}{100}s}{1983-661t^{2}}=\frac{100\left(t^{2}+2\right)}{1983-661t^{2}}$$

Dividing by -6.61t^{2}+19.83 undoes the multiplication by -6.61t^{2}+19.83.

$$s=\frac{100\left(t^{2}+2\right)}{1983-661t^{2}}$$

Solve for t

$$t=\sqrt{\frac{1983s-200}{661s+100}}$$

$$t=-\sqrt{\frac{1983s-200}{661s+100}}\text{, }s\geq \frac{200}{1983}\text{ or }s<-\frac{100}{661}$$