Question

Преобразуйте в дробь выражение

Answer 1

Объяснение:

a)

$\frac{x+2}{x+3} -\frac{x-1}{x} = \frac{x(x+2)- (x+3)(x-1) }{x(x+3) } = \frac{x^{2}+2x-x^{2} +x-3x+3}{x(x+3)} =\frac{3}{x^{2} +3x} ;$

б)

$2y-\frac{4y^{2} }{2y-1} -1 = \frac{(2y-1)^{2}-4y^{2} }{2y-1} = \frac{4y^{2} -4y+1- 4y^{2} }{2y-1} = \frac{1-4y}{2y-1} ;$

в)

$\frac{5a^{2} }{5ab-b^{2} } -\frac{b}{25a-5b} = \frac{5a^{2} }{b(5a-b)} -\frac{b}{5(5a-b)} = \frac{25a^{2} -b^{2} }{5b(5a-b)} = \frac{(5a-b)(5a+b)}{5b(5a-b)} =\frac{5a+b}{5b};$

г)

$\frac{x^{2} }{x^{3} -x} +\frac{1}{2-2x} = \frac{x^{2} }{x(x^{2} -1)} -\frac{1}{2(x-1)} =\frac{x^{2} }{x(x-1)(x+1) } -\frac{1}{2(x-1)} = \frac{2x^{2} -x^{2} -x}{2x(x-1)(x+1)} =\\\\\frac{x^{2} -x}{2x(x-1)(x+1)} =\frac{x(x-1)}{2x(x-1)(x+1) } =\frac{1}{2(x+1) } =\frac{1}{2x+2} .$