Solve FS=s^2+3/s^2+4s^2+6

$$F S = \frac { s ^ { 2 } + 3 } { s ^ { 2 } + 4 s ^ { 2 } + 6 }$$

Solve for F

$$F=\frac{s^{2}+3}{S\left(5s^{2}+6\right)}$$

$$S\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5s^{2}+6.

$$FS\left(5s^{2}+6\right)=s^{2}+3$$

Use the distributive property to multiply FS by 5s^{2}+6.

$$5FSs^{2}+6FS=s^{2}+3$$

Combine all terms containing F.

$$\left(5Ss^{2}+6S\right)F=s^{2}+3$$

Divide both sides by 5Ss^{2}+6S.

$$\frac{\left(5Ss^{2}+6S\right)F}{5Ss^{2}+6S}=\frac{s^{2}+3}{5Ss^{2}+6S}$$

Dividing by 5Ss^{2}+6S undoes the multiplication by 5Ss^{2}+6S.

$$F=\frac{s^{2}+3}{5Ss^{2}+6S}$$

Divide s^{2}+3 by 5Ss^{2}+6S.

$$F=\frac{s^{2}+3}{S\left(5s^{2}+6\right)}$$

Solve for S

$$S=\frac{s^{2}+3}{F\left(5s^{2}+6\right)}$$

$$F\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5s^{2}+6.

$$FS\left(5s^{2}+6\right)=s^{2}+3$$

Use the distributive property to multiply FS by 5s^{2}+6.

$$5FSs^{2}+6FS=s^{2}+3$$

Combine all terms containing S.

$$\left(5Fs^{2}+6F\right)S=s^{2}+3$$

Divide both sides by 6F+5Fs^{2}.

$$\frac{\left(5Fs^{2}+6F\right)S}{5Fs^{2}+6F}=\frac{s^{2}+3}{5Fs^{2}+6F}$$

Dividing by 6F+5Fs^{2} undoes the multiplication by 6F+5Fs^{2}.

$$S=\frac{s^{2}+3}{5Fs^{2}+6F}$$

Divide s^{2}+3 by 6F+5Fs^{2}.

$$S=\frac{s^{2}+3}{F\left(5s^{2}+6\right)}$$