66th Problem 2016

Algebra Level pending

Simplify:

a 3 − a 2 + a − 1 a 2 − 1 = ? \large\dfrac{a^3-a^2+a-1}{a^2-1} = \ ? \

Assume: a > 1 a>1

Check out the set: 2016 Problems

( a + 1 ) ( a − 1 ) (a+1)(a-1) a 3 − a 2 + a − 1 a 2 − 1 \large\frac{a^3-a^2+a-1}{a^2-1} a 2 + 1 a + 1 \large\frac{a^2+1}{a+1} a 2 + 1 a^2+1

Angela Fajardo by Angela Fajardo , 19, Philippines

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1 solution

Firstly we will factorise the numerator which gives us a 2 ( a − 1 ) + 1 ( a − 1 ) = ( a 2 + 1 ) ( a − 1 ) a^2 (a-1)+1 (a-1)=(a^2+1)(a-1) Now on factorising the denominator we have ( a + 1 ) ( a − 1 ) (a+1)(a-1) Now ( a − 1 ) (a-1) cancels out leaving us with a 2 + 1 a + 1 \frac {a^2+1}{a+1} which is the answer

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Moderator note:

Simple standard approach.

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