2 explanation
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Dyalog APL, 10 bytes

Does not even use a build-in for rationals.

Takes {a0,a1,a2,a3,...} as argument, returns {denominator,numerator}.

1(,÷∨)+∘÷/

1(,÷∨) 1-prepended-to divided by the GCD of 1 and

+∘÷ plus-the-reciprocal-of

/ reduction over

TryAPL online!

Dyalog APL, 10 bytes

Does not even use a build-in for rationals.

Takes {a0,a1,a2,a3,...} as argument, returns {denominator,numerator}.

1(,÷∨)+∘÷/

TryAPL online!

Dyalog APL, 10 bytes

Does not even use a build-in for rationals.

Takes {a0,a1,a2,a3,...} as argument, returns {denominator,numerator}.

1(,÷∨)+∘÷/

1(,÷∨) 1-prepended-to divided by the GCD of 1 and

+∘÷ plus-the-reciprocal-of

/ reduction over

TryAPL online!

1
source | link

Dyalog APL, 10 bytes

Does not even use a build-in for rationals.

Takes {a0,a1,a2,a3,...} as argument, returns {denominator,numerator}.

1(,÷∨)+∘÷/

TryAPL online!