1) 18 / (m³ + 3m² - 9m -18)
(или
18 / [ (m² - 9)*(m + 3) ];
18 / (m + 3)²*(m - 3) )
2) (x + 3) / (x² - 4)
3) 2 / (2a - 1)
-2 / (2a - 1);
2 / (1 - 2а)
в случае, если поменять выражения местами)
Объяснение:
1)
m / (m² + 6m+9) + (m -6) / (9 - m²) = m / (m + 3)² + (m -6) / (3 - m)(3 + m) = [ m*(3 - m) + (m -6)*(m + 3) ] / (m + 3)²*(3 - m) = [ 3m - m² + m² - 3m - 18 ] / [ (9 - m²)*(m + 3) ] = -18 / (9m + 18 -m³ - 3m²) = 18 / (m³ + 3m² - 9m -18)
2)
[(x + 6) / (4x + 8)] - [(x + 2) / (4x + 8)] + [5 / (x² - 4)] =
[(x + 6)*(x - 2) - (x + 2)*(x - 2) + 5*4] / [4*(x + 2)*(x - 2)] =
[ x² + 4x -12 - x² + 4 + 20] / [4*(x + 2)*(x - 2)] =
[ 4x + 12] / [4*(x + 2)*(x - 2)] =
[ 4*(x + 3) ] / [4*(x + 2)*(x - 2)] =
(x + 3) / (x² - 4)
3)
[(b - 4) / (2a - 1)] - [(b² -2b - 24) / (2ab - 4 -b + 8a)] =
[(b - 4) / (2a - 1)] - [(b² -2b - 24) / ( 2a*(b + 4) - (b + 4) )] =
[(b - 4) / (2a - 1)] - [(b² -2b - 24) / ( (b + 4)*(2a - 1) )] =
[(b - 4)*(b + 4) - b² +2b + 24] / [(b + 4)*(2a - 1)] =
[ b² - 16 - b² +2b + 24] / [(b + 4)*(2a - 1)] =
[ 2b + 8] / [(b + 4)*(2a - 1)] = [ 2*(b + 4) ] / [(b + 4)*(2a - 1)] =
2 / (2a - 1)
1) 18 / (m³ + 3m² - 9m -18)
(или
18 / [ (m² - 9)*(m + 3) ];
18 / (m + 3)²*(m - 3) )
2) (x + 3) / (x² - 4)
3) 2 / (2a - 1)
(или
-2 / (2a - 1);
2 / (1 - 2а)
в случае, если поменять выражения местами)
Объяснение:
1)
m / (m² + 6m+9) + (m -6) / (9 - m²) = m / (m + 3)² + (m -6) / (3 - m)(3 + m) = [ m*(3 - m) + (m -6)*(m + 3) ] / (m + 3)²*(3 - m) = [ 3m - m² + m² - 3m - 18 ] / [ (9 - m²)*(m + 3) ] = -18 / (9m + 18 -m³ - 3m²) = 18 / (m³ + 3m² - 9m -18)
2)
[(x + 6) / (4x + 8)] - [(x + 2) / (4x + 8)] + [5 / (x² - 4)] =
[(x + 6)*(x - 2) - (x + 2)*(x - 2) + 5*4] / [4*(x + 2)*(x - 2)] =
[ x² + 4x -12 - x² + 4 + 20] / [4*(x + 2)*(x - 2)] =
[ 4x + 12] / [4*(x + 2)*(x - 2)] =
[ 4*(x + 3) ] / [4*(x + 2)*(x - 2)] =
(x + 3) / (x² - 4)
3)
[(b - 4) / (2a - 1)] - [(b² -2b - 24) / (2ab - 4 -b + 8a)] =
[(b - 4) / (2a - 1)] - [(b² -2b - 24) / ( 2a*(b + 4) - (b + 4) )] =
[(b - 4) / (2a - 1)] - [(b² -2b - 24) / ( (b + 4)*(2a - 1) )] =
[(b - 4)*(b + 4) - b² +2b + 24] / [(b + 4)*(2a - 1)] =
[ b² - 16 - b² +2b + 24] / [(b + 4)*(2a - 1)] =
[ 2b + 8] / [(b + 4)*(2a - 1)] = [ 2*(b + 4) ] / [(b + 4)*(2a - 1)] =
2 / (2a - 1)