Question

Алгебра, 8 класс. 99 баллов.
1. $frac{a-3}{a+3} - frac{a+2}{a-2}$
2.$frac{p+2}{p+1} - frac{p+6}{p-3}$
3.$frac{x+4y}{5y(x+y)}- frac{x-y}{5y(x-4y)}$
4.$frac{d-c}{3c(2c+d)} + frac{2c-d}{3c(c+d)}$

Answer 1

1
$frac{a-3}{a+3}+ frac{a+2}{a-2}= frac{(a-3)(a-2)-(a+3)(a+2)}{(a+3)(a-2)} = frac{a^2-2a-3a+6-(a^2+2a+3a+6)}{a^2-2a+3a-6} =$
$=frac{-10a}{a^2+a-6} = -frac{10a}{a^2+a-6} .$
2
$frac{p+2}{p+1} - frac{p+6}{p-3} = frac{(p+2)(p-3)-(p+6)(p+1)}{(p+1)(p-3)} = frac{p^2-p-6-(p^2+7p+6)}{p^2-2p-3} = -frac{8p}{p^2-2p-3}$
3
$frac{1}{5y}*( frac{x+4y}{x+y}- frac{x-y}{x-4y} )= frac{1}{5y}* frac{(x+4y)(x-4y)-(x-y)(x+y)}{(x+y)(x-4y)} =$
$= frac{1}{5y} * frac{x^2-(4y)^2-(x^2-y^2)}{x^2-4xy+yx-4y^2} = frac{1}{5y} * frac{-15y^2}{x^2-3xy-4y^2} =- frac{3y}{x^2-3xy-4y^2}$
4
$frac{1}{3c} *( frac{d-c}{2c+d} + frac{2c-d}{c+d} )= frac{1}{3c} * frac{(d-c)(d+c)+(2c-d)(2c+d)}{(2c+d)(c+d)} = frac{1}{3c}* frac{d^2-c^2+4c^2-d^2}{2c^2+3cd+d^2} =$
$=frac{1}{3c}* frac{3c^2}{2c^2+3cd+d^2}= frac{c}{2c^2+3cd+d^2}$