Question

Сократите дроби:
12ab/4a
3c(1-c)/9c^2(c-1)
12x-3x^3/6x+6
y-3/y^2-6y+9
m^2-4/m^2+4m+4
5-3x/25-x^2+2x/25-x^2

Answer 1

1)
$\frac{12ab}{4a} = 3b$
2)
$\frac{3c(1 - c)}{9c {}^{2}(c - 1) } = - \frac{3c(c - 1)}{9c {}^{2}(c - 1) } = - \frac{1}{3c}$
3)
$\frac{12x - 3x {}^{3} }{6x + 6} = \frac{3x(4 - x {}^{2} )}{6(x + 1)} = \\ = \frac{3x(2 - x)(2 + x)}{6(x + 1)} = \\ = \frac{x( 4- x {}^{2}) }{2(x + 1)}$
4)
$\frac{y - 3}{y {}^{2} - 6y + 9} = \frac{y - 3}{(y - 3)(y - 3)} = \frac{1}{y - 3}$
5)
$\frac{m {}^{2} - 4}{m {}^{2} + 4m + 4} = \frac{(m - 2)(m + 2)}{(m + 2) {}^{2} } = \frac{m - 2}{m + 2}$
6)
$\frac{5 - 3x}{25 - x {}^{2} } + \frac{2x}{25 - x {}^{2} } = \\ = \frac{5 - 3x + 2x}{25 - x {}^{2} } = \\ = \frac{5 - x}{(5 - x)(5 + x)} = \frac{1}{5 + x}$