What is y^4((2x^2)/(y^2)+1) ?

The solution to y^4((2x^2)/(y^2)+1) is y^2(y^2+2x^2)

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simplify y^4((2x^2)/(y^2)+1)

simplify

y^{4} (\frac{2 x ^{2}}{y ^{2}} + 1)

y^{2} (y^{2} + 2 x^{2})

Solution steps

y^{4} (\frac{2 x ^{2}}{y ^{2}} + 1)

Join

\frac{2 x ^{2}}{y ^{2}} + 1 : \frac{y ^{2} + 2 x ^{2}}{y ^{2}}

= y^{4} \frac{y ^{2} + 2 x ^{2}}{y ^{2}}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{y ^{4} ( y ^{2} + 2 x ^{2} )}{y ^{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

y^{4} = y^{2} y^{2}

= \frac{y ^{2} y ^{2} ( y ^{2} + 2 x ^{2} )}{y ^{2}}

Cancel the common factor:

y^{2}

= y^{2} (y^{2} + 2 x^{2})

(2 x + y) d x + (2 y e^{\frac{y}{x}} - x) d y

(x + i x^{2})^{2} - 2 (x + i x^{2}) (1 + 2 i x)

\frac{2 - e ^{- 3 π s}}{s ( s ^{2} + 1 )}

\frac{100 ( 0.02 x + 4 ) ^{3}}{x}

(f \circ g) (2 x - 1) (- x^{2})

What is y^4((2x^2)/(y^2)+1) ?
The solution to y^4((2x^2)/(y^2)+1) is y^2(y^2+2x^2)