Question

Упростите рациональные алгебраические выражения

Answer 1

$13.~~ \dfrac{a - 2}{2} - \dfrac{a - 3}{3} - 1 = \dfrac{3\cdot (a - 2) -2\cdot (a - 3) - 2\cdot 3}{2\cdot 3} = \\ \\=\dfrac{3a - 6-2a +6 - 6}{2\cdot 3} = \dfrac{a - 6}6 ;$

$15.~~ \dfrac{(x + 3)^2}{2x - 4} :\dfrac{3x+9}{x^2-4} = \dfrac{(x + 3)^2}{2(x-2)} :\dfrac{3(x+3)}{(x-2)\cdot (x + 2)} = \\ \\= \dfrac{(x + 3)^2\cdot (x - 2) \cdot (x+2)}{2(x-2)\cdot 3(x + 3)} = \dfrac{(x+3)(x + 2)}{6} = \dfrac{x^2 + 5x +6 }{6} ;$

$17. ~~\dfrac{42}{4a^2-9} +\dfrac{8}{2a+3}+ \dfrac{7}{3-2a} =\\ \\ = ~\dfrac{42}{(2a + 3)(2a - 3)} +\dfrac{8}{2a+3}- \dfrac{7}{2a-3} = \\ \\ = \dfrac{42 + 8\cdot (2a-3)-7\cdot (2a + 3)}{(2a + 3)(2a - 3)} = \\ \\= \dfrac{42 + 16a - 24 - 14a-21}{(2a + 3)(2a - 3)} =\dfrac{2a-3}{(2a + 3)(2a - 3)} = \dfrac{1}{2a+3} ;$