Алгебра, помогите, даю 35 баллов, решите от 141 по 150 задачи

141. [latex]( \frac{a}{a-b} + \frac{a}{b}) : \frac{a}{a-b} = \frac{ab+a^2-ab}{b(a-b)} : \frac{a}{a-b} = \frac{a^2}{b(a-b)} : \frac{a}{a-b} = \frac{a^2(a-b)}{ab(a-b)} = \frac{a}{b} [/latex] 142. [latex](\frac{c}{b-c} - \frac{c}{b}) : \frac{c^2}{b^2} = ( \frac{bc-c(b-c)}{b(b-c)} ) : \frac{c^2}{b^2} = \frac{bc-c}{b} : \frac{c^2}{b^2} = \frac{c(b-1)*b*b}{b*c*c} = \frac{b(b-1)}{c} [/latex] 143. [latex](\frac{1}{b^2} - \frac{1}{a^2}) * \frac{ab}{a+b} = ( \frac{a^2-b^2}{a^2b^2} )* \frac{ab}{a+b} = \frac{(a-b)(a+b)}{a*a*b*b} * \frac{ab}{a+b} = \frac{ab(a-b)(a+b)}{ab*ab(a+b)} = \frac{a-b}{ab} [/latex] 144. [latex]( \frac{a}{b} - \frac{b}{a}) * \frac{b}{a-b} = \frac{a^2-b^2}{ab} * \frac{b}{a-b} = \frac{(a-b)(a+b)}{ab} * \frac{b}{a-b} = \frac{b(a-b)(a+b)}{ab(a-b)} = \frac{(a+b)}{a} [/latex] 145. [latex] \frac{a^2-4}{a} * \frac{1}{a+2} - \frac{a+2}{a} = \frac{(a-2)(a+2)}{a(a+2)} - \frac{a+2}{a} = \frac{a-2}{a} - \frac{a+2}{a} = \frac{a-2-a-2}{a} = - \frac{4}{a} [/latex] 146. [latex] \frac{c-3}{c} - \frac{c^2-9}{c} * \frac{1}{c-3} = \frac{c-3}{c} - \frac{(c-3)(c+3)}{c} * \frac{1}{c-3} = \frac{c-3}{c} - \frac{(c-3)(c+3)}{c(c-3)} = [/latex][latex]\frac{c-3}{c} - \frac{c+3}{c} = \frac{c-3-c-3}{c} = - \frac{6}{c} [/latex] 147. [latex] \frac{a-1}{a^2} * \frac{ax-a}{a-1} + \frac{1-x}{2a} = \frac{a(a-1)(x-1)}{a^2(a-1)} + \frac{1-x}{2a} = \frac{x-1}{a} + \frac{x-1}{2a} = \frac{2x-2+x-1}{2a} = [/latex][latex] \frac{3x-3}{2a} = \frac{3(x-1)}{2a} [/latex] 148. [latex] \frac{x^2-xy}{y-1} * \frac{y-1}{x^2} + \frac{y-x}{2x} = \frac{x(x-y)(y-1)}{x^2(y-1)} + \frac{y-x}{2x} = \frac{x-y}{x} + \frac{y-x}{2x} = \frac{2x-2y+y-x}{2x} [/latex][latex]= \frac{x-y}{2x} [/latex] 149. [latex] \frac{x}{a} - \frac{x^2-a^2}{a^2} * \frac{a}{x+a} = \frac{x}{a} - \frac{a(x-a)(x+a)}{a^2(x+a)} = \frac{x}{a} - \frac{x-a}{a} = \frac{x-x+a}{a} = 1 [/latex] 150. [latex]b - \frac{2a}{a-b} * \frac{a^2 - b^2}{4a} = b - \frac{2a(a-b)(a+b)}{4a(a-b)} = b - \frac{a+b}{2} = 2b - a - b = b-a [/latex] Удачи!