Question

Cократите дробь
1) 4x^2−x/ 6x
2) 49x^2−36y^2/ 6y+7x
3) 15x^4 y^3 z^9/ 5x^3 y^2 z^4
4) 25a^2−10b^2/ (4b−5a)^2
5) 9y−9z/ 15xz−15xy
30 Баллов

Answer 1

$\displaystyle\bf\\1)\\\\\frac{4x^{2} -x}{6x} =\frac{x\cdot(4x-1)}{6x} =\frac{4x-1}{6} \\\\\\2)\\\\\frac{49x^{2} -36y^{2} }{6y+7x} =\frac{(7x)^{2} -(6y)^{2} }{6y+7x} =\frac{(7x-6y)(7x+6y)}{6y+7x} =7x-6y\\\\\\3)\\\\\frac{15x^{4} y^{3} z^{9} }{5x^{3} y^{2} z^{4} } =\frac{3\cdot 5\cdot x^{3}\cdot x\cdot y^{2} \cdot y\cdot z^{4} \cdot z^{5} }{5x^{3} y^{2} z^{4} } =3xyz^{5}$

$\displaystyle\bf\\4)\\\\\frac{25a^{2} -16b^{2} }{(4b-5a)^{2} } =\frac{(5a-4b)(5a+4b)}{(5a-4b)^{2} } =\frac{5a+4b}{5a-4b} \\\\\\5)\\\\\frac{9y-9z}{15xz-15xy} =\frac{9(y-z)}{15x(z-y)} =-\frac{3}{5x}$