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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 8: Rút gọn ($\frac{2xy}{x^2-y^2}$ + $\frac{x-y}{2x+2y}$) : $\frac{x+y}{2x}$ + $\frac{y}{y-x}$

Toán Lớp 8: Rút gọn
($\frac{2xy}{x^2-y^2}$ + $\frac{x-y}{2x+2y}$) : $\frac{x+y}{2x}$ + $\frac{y}{y-x}$

Comments ( 2 )

1. Giải đáp:
$=-\frac{x\left(x+y\right)}{y^2-x^2+2xy}$
Lời giải và giải thích chi tiết:
$\left(\frac{2xy}{x^2-y^2}+\frac{x-y}{2x+2y}\right)\div \frac{x+y}{2x}+\frac{y}{y-x}$
$=\frac{x^3+3xy^2+y^3+3x^2y}{\left(2x+2y\right)\left(x^2-y^2\right)} \div \frac{x+y}{2x}+\frac{y}{y-x}$
$=\frac{x^3+3xy^2+y^3+3x^2y}{\left(2x+2y\right)\left(x^2-y^2\right)}\div \frac{y^2-x^2+2xy}{2x\left(y-x\right)}$
$=\frac{\left(x^3+3xy^2+y^3+3x^2y\right).2x\left(y-x\right)}{\left(2x+2y\right)\left(x^2-y^2\right)\left(y^2-x^2+2xy\right)}$
$=-\frac{x\left(x+y\right)}{y^2-x^2+2xy}$

2. ( \frac{2xy}{x^2-y^2} + \frac{x-y}{2x+2y} ) : \frac{x+y}{2x} + \frac{y}{y-x}        ( x \ne 0 ; x \ne ± y )
= [ \frac{2xy}{(x-y)(x+y)} + \frac{x-y}{2 (x+y) } ] . \frac{2x}{x+y} – \frac{y}{x-y}
= \frac{4xy+x^2-2xy+y^2}{2(x-y)(x+y)} . \frac{2x}{x+y} – \frac{y}{x-y}
= \frac{x^2+2xy+y^2}{2(x-y)(x+y)} . \frac{2x}{x+y} – \frac{y}{x-y}
= \frac{(x+y)^2}{2(x-y)(x+y)} . \frac{2x}{x+y} – \frac{y}{x-y}
= \frac{x}{x-y} – \frac{y}{x-y}
= \frac{x-y}{x-y}
= 1