Simplify (1/(b^2)+a^2)/(1/(a^2)+b^2)

$\frac{\frac{1}{b^{2}} + a^{2}}{\frac{1}{a^{2}} + b^{2}}$

Multiply the numerator and denominator of the complex fraction by $b^{2} a^{2}$ .

Multiply $\frac{\frac{1}{b^{2}} + a^{2}}{\frac{1}{a^{2}} + b^{2}}$ by $\frac{b^{2} a^{2}}{b^{2} a^{2}}$ .

$\frac{b^{2} a^{2}}{b^{2} a^{2}} \cdot \frac{\frac{1}{b^{2}} + a^{2}}{\frac{1}{a^{2}} + b^{2}}$

Combine.

$\frac{b^{2} a^{2} (\frac{1}{b^{2}} + a^{2})}{b^{2} a^{2} (\frac{1}{a^{2}} + b^{2})}$

Apply the distributive property.

$\frac{b^{2} a^{2} \frac{1}{b^{2}} + b^{2} a^{2} a^{2}}{b^{2} a^{2} \frac{1}{a^{2}} + b^{2} a^{2} b^{2}}$

Simplify by cancelling.

Cancel the common factor of $b^{2}$ .

Factor $b^{2}$ out of $b^{2} a^{2}$ .

$\frac{b^{2} (a^{2}) \frac{1}{b^{2}} + b^{2} a^{2} a^{2}}{b^{2} a^{2} \frac{1}{a^{2}} + b^{2} a^{2} b^{2}}$

Cancel the common factor.

$\frac{b^{2} a^{2} \frac{1}{b^{2}} + b^{2} a^{2} a^{2}}{b^{2} a^{2} \frac{1}{a^{2}} + b^{2} a^{2} b^{2}}$

Rewrite the expression.

$\frac{a^{2} + b^{2} a^{2} a^{2}}{b^{2} a^{2} \frac{1}{a^{2}} + b^{2} a^{2} b^{2}}$

Cancel the common factor of $a^{2}$ .

Factor $a^{2}$ out of $b^{2} a^{2}$ .

$\frac{a^{2} + b^{2} a^{2} a^{2}}{a^{2} b^{2} \frac{1}{a^{2}} + b^{2} a^{2} b^{2}}$

Cancel the common factor.

$\frac{a^{2} + b^{2} a^{2} a^{2}}{a^{2} b^{2} \frac{1}{a^{2}} + b^{2} a^{2} b^{2}}$

Rewrite the expression.

$\frac{a^{2} + b^{2} a^{2} a^{2}}{b^{2} + b^{2} a^{2} b^{2}}$

Simplify terms.

Factor $a^{2}$ out of $a^{2} + b^{2} a^{2} a^{2}$ .

Multiply by $1$ .

$\frac{a^{2} \cdot 1 + b^{2} a^{2} a^{2}}{b^{2} + b^{2} a^{2} b^{2}}$

Factor $a^{2}$ out of $b^{2} a^{2} a^{2}$ .

$\frac{a^{2} \cdot 1 + a^{2} (b^{2} a^{2})}{b^{2} + b^{2} a^{2} b^{2}}$

Factor $a^{2}$ out of $a^{2} \cdot 1 + a^{2} (b^{2} a^{2})$ .

$\frac{a^{2} (1 + b^{2} a^{2})}{b^{2} + b^{2} a^{2} b^{2}}$

Factor $b^{2}$ out of $b^{2} + b^{2} a^{2} b^{2}$ .

Multiply by $1$ .

$\frac{a^{2} (1 + b^{2} a^{2})}{b^{2} \cdot 1 + b^{2} a^{2} b^{2}}$

Factor $b^{2}$ out of $b^{2} a^{2} b^{2}$ .

$\frac{a^{2} (1 + b^{2} a^{2})}{b^{2} \cdot 1 + b^{2} (a^{2} b^{2})}$

Factor $b^{2}$ out of $b^{2} \cdot 1 + b^{2} (a^{2} b^{2})$ .

$\frac{a^{2} (1 + b^{2} a^{2})}{b^{2} (1 + a^{2} b^{2})}$

Reorder the terms.

$\frac{a^{2} (a^{2} b^{2} + 1)}{b^{2} (a^{2} b^{2} + 1)}$

Cancel the common factor of $a^{2} b^{2} + 1$ .

Cancel the common factor.

$\frac{a^{2} (a^{2} b^{2} + 1)}{b^{2} (a^{2} b^{2} + 1)}$

Rewrite the expression.

$\frac{a^{2}}{b^{2}}$