Solve quadratic fractionI would like to simplify the fraction x 2 − 2 x x...

enrotlavaec

enrotlavaec

Answered

2022-06-24

Solve quadratic fraction
I would like to simplify the fraction
x 2 2 x x 2 + x 6
I know from Mathematica that it should equal 3 3 x but how do I get there?

Answer & Explanation

humusen6p

humusen6p

Expert

2022-06-25Added 22 answers

The numerator factors as x 2 2 x = x ( x 2 )
By the quadratic formula, the denominator has roots 2 and 3. So the denominator factors as x 2 + x 6 = ( x 2 ) ( x + 3 )
Hence x 2 2 x x 2 + x 6 = x ( x 2 ) ( x 2 ) ( x + 3 ) = x x + 3
crossoverman9b

crossoverman9b

Expert

2022-06-26Added 5 answers

x 2 + x 6 = ( x 2 ) ( x + 3 ) x ( x 2 ) ( x + 3 ) ( x 2 ) = x x + 3 , so your result is incorrect, as the next counterexample shows:
x = 1 ; x 2 2 x x 2 + x 6 = 1 4 1 = 3 3 x

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