solve: (4+x) (5-x)=1/(2+x) (7-x)
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( 4 + x ) ( 5 - x ) = 1 / ( 2 + x ) ( 7 - x )
( 4 + x ) ( 5 - x ) ( 2 + x ) ( 7 - x ) = 1
[4 ( 5 - x ) + x ( 5 - x ) ] [ 2 ( 7 - x ) + x ( 7 - x ) ] = 1
[ 20 - 4x + 5x -x² ] [ 14 - 7x + 7x -x² ] = 1
[ 20 + x - x ² ] [ 14 - x² ] = 1
14 [ 20 + x - x ² ] - x² [ 20 + x - x ² ] = 1
280 + 14x - 14x² - 20x² - x³ + x^4 = 1
280 + 14x - 34x² - x³+ x^4 = 1
14x - 34x² - x³+ x^4 = 1 - 280
x^4 - x³ - 34x² + 14x = -279
( 4 + x ) ( 5 - x ) ( 2 + x ) ( 7 - x ) = 1
[4 ( 5 - x ) + x ( 5 - x ) ] [ 2 ( 7 - x ) + x ( 7 - x ) ] = 1
[ 20 - 4x + 5x -x² ] [ 14 - 7x + 7x -x² ] = 1
[ 20 + x - x ² ] [ 14 - x² ] = 1
14 [ 20 + x - x ² ] - x² [ 20 + x - x ² ] = 1
280 + 14x - 14x² - 20x² - x³ + x^4 = 1
280 + 14x - 34x² - x³+ x^4 = 1
14x - 34x² - x³+ x^4 = 1 - 280
x^4 - x³ - 34x² + 14x = -279
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