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

Math
1+a(1+a2)12a+(1+a2)12
Multiply the numerator and denominator of the complex fraction by (1+a2)12.
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Multiply 1+a(1+a2)12a+(1+a2)12 by (1+a2)12(1+a2)12.
(1+a2)12(1+a2)12⋅1+a(1+a2)12a+(1+a2)12
Combine.
(1+a2)12(1+a(1+a2)12)(1+a2)12(a+(1+a2)12)
(1+a2)12(1+a(1+a2)12)(1+a2)12(a+(1+a2)12)
Apply the distributive property.
(1+a2)12⋅1+(1+a2)12a(1+a2)12(1+a2)12a+(1+a2)12(1+a2)12
Reduce the expression by cancelling the common factors.
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Cancel the common factor of (1+a2)12.
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Cancel the common factor.
(1+a2)12⋅1+(1+a2)12a(1+a2)12(1+a2)12a+(1+a2)12(1+a2)12
Rewrite the expression.
(1+a2)12⋅1+a(1+a2)12a+(1+a2)12(1+a2)12
(1+a2)12⋅1+a(1+a2)12a+(1+a2)12(1+a2)12
Multiply (1+a2)12 by 1.
(1+a2)12+a(1+a2)12a+(1+a2)12(1+a2)12
(1+a2)12+a(1+a2)12a+(1+a2)12(1+a2)12
Simplify the denominator.
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Multiply (1+a2)12 by (1+a2)12 by adding the exponents.
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Use the power rule aman=am+n to combine exponents.
(1+a2)12+a(1+a2)12a+(1+a2)12+12
Combine the numerators over the common denominator.
(1+a2)12+a(1+a2)12a+(1+a2)1+12
Add 1 and 1.
(1+a2)12+a(1+a2)12a+(1+a2)22
Divide 2 by 2.
(1+a2)12+a(1+a2)12a+(1+a2)1
(1+a2)12+a(1+a2)12a+(1+a2)1
Simplify (1+a2)1.
(1+a2)12+a(1+a2)12a+1+a2
Reorder terms.
(1+a2)12+aa2+a(1+a2)12+1
(1+a2)12+aa2+a(1+a2)12+1
Simplify (1+a/((1+a^2)^(1/2)))/(a+(1+a^2)^(1/2))

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