Solve 3^2-3^-2/3^2+3^-2

$$\frac { 3 ^ { 2 } - 3 ^ { - 2 } } { 3 ^ { 2 } + 3 ^ { - 2 } }$$

Evaluate

$$\frac{40}{41}\approx 0.975609756$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\frac{9-3^{-2}}{3^{2}+3^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{9-\frac{1}{9}}{3^{2}+3^{-2}}$$

Subtract \frac{1}{9} from 9 to get \frac{80}{9}.

$$\frac{\frac{80}{9}}{3^{2}+3^{-2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{80}{9}}{9+3^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{80}{9}}{9+\frac{1}{9}}$$

Add 9 and \frac{1}{9} to get \frac{82}{9}.

$$\frac{\frac{80}{9}}{\frac{82}{9}}$$

Divide \frac{80}{9} by \frac{82}{9} by multiplying \frac{80}{9} by the reciprocal of \frac{82}{9}.

$$\frac{80}{9}\times \frac{9}{82}$$

Multiply \frac{80}{9} and \frac{9}{82} to get \frac{40}{41}.

$$\frac{40}{41}$$

Factor

$$\frac{2 ^ {3} \cdot 5}{41} = 0.975609756097561$$