Example

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

Question

$$y^{\prime}=\frac{2(x^{2}+1)-4x^{2}}{(x^{2}+1)^{2}}=$$

Answer

$$y=2^(1/prime)*(x^2+1)^(1/prime)*(1-2*x^2*(x^2+1))^(1/prime)$$

Solution


Take the \((prime)\)th root of both sides.
\[y=\sqrt[prime]{2({x}^{2}+1)-4{x}^{2}{({x}^{2}+1)}^{2}}\]
Factor out the common term \(2({x}^{2}+1)\).
\[y=\sqrt[prime]{2({x}^{2}+1)(1-2{x}^{2}({x}^{2}+1))}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[y=\sqrt[prime]{2}\sqrt[prime]{{x}^{2}+1}\sqrt[prime]{1-2{x}^{2}({x}^{2}+1)}\]
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