perplexus.info :: Just Math : Quadratic fractions

Quadratic fractions (Posted on 2025-04-10)

Find the sum of the real values of x satisfying

2x² + 20x + 21    2x² + 24x + 11
-------------- = ---------------
2x² − 12x + 20    2x² − 8x + 10

No Solution Yet Submitted by Danish Ahmed Khan

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re(2): solution, maybe

| Comment 3 of 4 |

(In reply to re: solution, maybe by Steven Lord)

xdog's math is OK until (-32x-1)/A=(-32x-1)/B or A=B.

Dividing by (-32x-1) is only valid if (-32x-1) <> 0.

The next step after (-32x-1)/A=(-32x-1)/B or A=B

should say: A=B or (-32x-1) = 0.

This then gives rise to two solutions, x = 5/2 and x = -1/32

Posted by Steve Herman on 2025-04-11 06:35:00

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