Solve psi/t^2=1+t^2/4/t^2+4

$$\frac { \psi } { t ^ { 2 } } = \frac { 1 + \frac { t ^ { 2 } } { 4 } } { t ^ { 2 } + 4 }$$

Solve for ψ

$$\psi =\frac{t^{2}}{4}$$

$$t\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by t^{2}\left(t^{2}+4\right), the least common multiple of t^{2},t^{2}+4.

$$\left(t^{2}+4\right)\psi =t^{2}\left(1+\frac{t^{2}}{4}\right)$$

Use the distributive property to multiply t^{2}+4 by \psi .

$$t^{2}\psi +4\psi =t^{2}\left(1+\frac{t^{2}}{4}\right)$$

Use the distributive property to multiply t^{2} by 1+\frac{t^{2}}{4}.

$$t^{2}\psi +4\psi =t^{2}+t^{2}\times \frac{t^{2}}{4}$$

Express t^{2}\times \frac{t^{2}}{4} as a single fraction.

$$t^{2}\psi +4\psi =t^{2}+\frac{t^{2}t^{2}}{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$t^{2}\psi +4\psi =t^{2}+\frac{t^{4}}{4}$$

Multiply both sides of the equation by 4.

$$4t^{2}\psi +16\psi =4t^{2}+t^{4}$$

Combine all terms containing \psi .

$$\left(4t^{2}+16\right)\psi =4t^{2}+t^{4}$$

The equation is in standard form.

$$\left(4t^{2}+16\right)\psi =t^{4}+4t^{2}$$

Divide both sides by 4t^{2}+16.

$$\frac{\left(4t^{2}+16\right)\psi }{4t^{2}+16}=\frac{t^{2}\left(t^{2}+4\right)}{4t^{2}+16}$$

Dividing by 4t^{2}+16 undoes the multiplication by 4t^{2}+16.

$$\psi =\frac{t^{2}\left(t^{2}+4\right)}{4t^{2}+16}$$

Divide \left(4+t^{2}\right)t^{2} by 4t^{2}+16.

$$\psi =\frac{t^{2}}{4}$$

Solve for t

$$t=2\sqrt{\psi }$$

$$t=-2\sqrt{\psi }\text{, }\psi >0$$