ĐKXĐ: \(\left\{{}\begin{matrix}3x\ne-y\\3x\ne y\end{matrix}\right.\)

a. \(\dfrac{x}{3x+y}+\dfrac{x}{3x-y}-\dfrac{2xy}{y^2-9x^2}\)

\(=\dfrac{x.\left(3x-y\right)}{\left(3x+y\right).\left(3x-y\right)}+\dfrac{x.\left(3x+y\right)}{\left(3x+y\right).\left(3x-y\right)}+\dfrac{2xy}{9x^2-y^2}\)

\(=\dfrac{x.\left(3x+y+3x-y\right)+2xy}{\left(3x-y\right).\left(3x+y\right)}\)

\(=\dfrac{6x^2+2xy}{\left(3x-y\right).\left(3x+y\right)}\)

\(=\dfrac{2x\left(3x+y\right)}{\left(3x+y\right).\left(3x-y\right)}\)

\(=\dfrac{2x}{3x-y}\)

ĐKXĐ: \(\left\{{}\begin{matrix}x\ne0\\x\ne-5\end{matrix}\right.\)

b. \(\dfrac{4x+5}{x^2+5x}-\dfrac{3}{x+5}\)

\(=\dfrac{4x+5}{x.\left(x+5\right)}-\dfrac{3x}{x.\left(x+5\right)}\)

\(=\dfrac{x+5}{x.\left(x+5\right)}\)

\(=\dfrac{1}{x}\)

a) Ta có: \(\dfrac{x}{3x+y}+\dfrac{x}{3x-y}-\dfrac{2xy}{y^2-9x^2}\)

\(=\dfrac{x\left(3x-y\right)}{\left(3x+y\right)\left(3x-y\right)}+\dfrac{x\left(3x+y\right)}{\left(3x+y\right)\left(3x-y\right)}+\dfrac{2xy}{\left(3x+y\right)\left(3x-y\right)}\)

\(=\dfrac{3x^2-xy+3x^2+xy+2xy}{\left(3x+y\right)\left(3x-y\right)}\)

\(=\dfrac{6x^2+2xy}{\left(3x+y\right)\left(3x-y\right)}\)

\(=\dfrac{2x\left(3x+y\right)}{\left(3x+y\right)\left(3x-y\right)}\)

\(=\dfrac{2x}{3x-y}\)

b) Ta có: \(\dfrac{4x+5}{x^2+5x}-\dfrac{3}{x+5}\)

\(=\dfrac{4x+5}{x\left(x+5\right)}-\dfrac{3x}{x\left(x+5\right)}\)

\(=\dfrac{4x+5-3x}{x\left(x+5\right)}\)

\(=\dfrac{x+5}{x\left(x+5\right)}\)

\(=\dfrac{1}{x}\)

Lời giải:

 $\frac{x}{y}=\frac{2}{3}\Rightarrow \frac{x}{2}=\frac{y}{3}$. Đặt $\frac{x}{2}=\frac{y}{3}=k$ thì:

$x=2k; y=3k$

Khi đó: $3x-2y=3.2k-3.2k=0$. Mẫu số không thể bằng $0$ nên $A$ không xác định. Bạn xem lại.

$B=\frac{2(2k)^2-2k.3k+3(3k)^2}{3(2k)^2+2.2k.3k+(3k)^2}=\frac{29k^2}{33k^2}=\frac{29}{33}$

kha sdaif dòng mik xin phép trình bày bằng lời ạ :

a) tìm MTC rồi quy đồng lên làm bình thường ại , tử cộng tử mấu giữ nguyên 

b) cx vậy ạ tách mẫu tìm MTC rồi ....

~ hok tốt ~

a: =>A-B=3x^2y-4xy^2+x^2y-2xy^2=4x^2y-6xy^2

b: =>B-A=-7xy^2+8x^2y-5xy^2+6x^2y=-12xy^2+14x^2y

=>A-B=12xy^2-14x^2y

c: =>B-A=8x^2y^3-4x^3y-3x^2y^3+5x^3y^2=5x^2y^3+x^3y^2

=>A-B=-5x^2y^3-x^3y^2

d: =>A-B=2x^2y^3-7x^3y+6x^2y^3+3x^3y^2=8x^2y^3-7x^3y+3x^3y^2