Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\frac{(x^{2}-\frac{1}{y^{2}})^{x}(x-\frac{1}{y})^{y-x}}{(y^{2}-\frac{1}{x^{2}})^{y}(y+\frac{1}{x})^{y-y}}$$

Answer

$$((x^2-1/y^2)^x*(x-1/y)^(y-x))/(y^2-1/x^2)^y$$

Solution


Simplify  \(y-y\)  to  \(0\).
\[\frac{{({x}^{2}-\frac{1}{{y}^{2}})}^{x}{(x-\frac{1}{y})}^{y-x}}{{({y}^{2}-\frac{1}{{x}^{2}})}^{y}{(y+\frac{1}{x})}^{0}}\]
Use Rule of Zero: \({x}^{0}=1\).
\[\frac{{({x}^{2}-\frac{1}{{y}^{2}})}^{x}{(x-\frac{1}{y})}^{y-x}}{{({y}^{2}-\frac{1}{{x}^{2}})}^{y}\times 1}\]
Simplify  \({({y}^{2}-\frac{1}{{x}^{2}})}^{y}\times 1\)  to  \({({y}^{2}-\frac{1}{{x}^{2}})}^{y}\).
\[\frac{{({x}^{2}-\frac{1}{{y}^{2}})}^{x}{(x-\frac{1}{y})}^{y-x}}{{({y}^{2}-\frac{1}{{x}^{2}})}^{y}}\]
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