What is (v^4+4v^2+4)/(4-v^4) ?

The solution to (v^4+4v^2+4)/(4-v^4) is (v^2+2)/(2-v^2)

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simplify (v^4+4v^2+4)/(4-v^4)

simplify

\frac{v ^{4} + 4 v ^{2} + 4}{4 - v ^{4}}

\frac{v ^{2} + 2}{2 - v ^{2}}

Solution steps

\frac{v ^{4} + 4 v ^{2} + 4}{4 - v ^{4}}

Factor

v^{4} + 4 v^{2} + 4 : (v^{2} + 2)^{2}

= \frac{( v ^{2} + 2 ) ^{2}}{4 - v ^{4}}

Factor

4 - v^{4} : (2 + v^{2}) (2 - v^{2})

= \frac{( v ^{2} + 2 ) ^{2}}{( 2 + v ^{2} ) ( 2 - v ^{2} )}

Apply the commutative law:

2 + v^{2} = v^{2} + 2

= \frac{( v ^{2} + 2 ) ^{2}}{( v ^{2} + 2 ) ( 2 - v ^{2} )}

Apply exponent rule:

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

(v^{2} + 2)^{2} = (v^{2} + 2) (v^{2} + 2)

= \frac{( v ^{2} + 2 ) ( v ^{2} + 2 )}{( v ^{2} + 2 ) ( 2 - v ^{2} )}

Cancel the common factor:

v^{2} + 2

= \frac{v ^{2} + 2}{2 - v ^{2}}

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What is (v^4+4v^2+4)/(4-v^4) ?
The solution to (v^4+4v^2+4)/(4-v^4) is (v^2+2)/(2-v^2)