Question

Помогите решить алгебраические выражения
1)(1/х-2)+(х/-х+2)
2)(3х+1/х+1)+(3+х/х+1)
3)(5х+1/х)-(1-6/х-1)
4)(4х/х)+(1+5х/х)
5)(7с-1/х²)-(с²-с/х-с)

Answer 1

$1)\; \frac{1}{x-2} + \frac{x}{-x+2} = \frac{1}{x-2} - \frac{x}{x-2} = \frac{1-x}{x-2} =-\frac{x-1}{x-2}\\\\2)\; \frac{3x+1}{x+1} + \frac{3+x}{x+1} = \frac{3x+1+3+x}{x+1} = \frac{4x+4}{x+1} = \frac{4(x+1)}{x+1} =4\\\\3)\; \frac{5x+1}{x-1} - \frac{6}{x-1} = \frac{5x+1-6}{x-1} = \frac{5x-5}{x-1} = \frac{5(x-1)}{x-1} =5\\\\4)\; \frac{4x}{x} + \frac{1+5x}{x} = \frac{4x+1+5x}{x} =\frac{9x+1}{x} =9+\frac{1}{x}$

$5)\; \frac{7c-1}{x^2-c^2} - \frac{c}{x-c} = \frac{(7c-1)-c(x+c)}{(x-c)(x+c)} = \frac{7c-1-cx-c^2}{(x-c)(x+c)}$