cộng trừ các phân thức
\(\frac{x}{x-2y}+\frac{x}{x+2y}+\frac{8x^2}{4xy^2-x^3}\)
cộng trừ các phân thức
\(\frac{2x^2-11x}{2xy}+\frac{5y-x}{y}+\frac{x+2y}{x}\)
\(\frac{2x^2-11x}{2xy}+\frac{5y-x}{y}+\frac{x+2y}{x}\)
\(=\frac{2x^2-11x+\left(5y-x\right)2x+\left(x+2y\right)2y}{2xy}\)
\(=\frac{2x^2-11x+10xy-2x^2+2xy+4y^2}{2xy}=\frac{12xy-11x+4y^2}{2xy}\)
cộng trừ các phân thức
\(\frac{3}{4xy}+\frac{5x}{2y^2z}+\frac{7}{6yz^2}\)
\(\frac{3}{4xy}+\frac{5x}{2y^2z}+\frac{7}{6yz^2}\)
\(=\frac{9yz^2}{12xy^2z^2}+\frac{30x^2z}{12xy^2z^2}+\frac{14xy}{12xy^2z^2}\)
\(=\frac{9yz^2+30x^2z+14xy}{12xy^2z^2}\)
cộng trừ các phân thức
\(x+y+\frac{3x^2}{2y}\)
\(x+y+\frac{3x^2}{2y}\)
\(=\frac{2xy}{2y}+\frac{2y^2}{2y}+\frac{3x^2}{2y}=\frac{2xy+2y^2+3x^2}{2y}=\frac{2y.\left(2x+y\right)+3x^2}{2y}=\frac{2x+y+3x^2}{2y}\)
p/s: mới lớp 7 ạ sai sót bỏ qua nha :>
aeeeeei nhầm nha :>
\(\frac{2xy}{2y}+\frac{2y^2}{2y}+\frac{3x^2}{2y}=\frac{2xy+2y^2+3x^2}{2y}=\frac{2y.\left(x+y\right)+3x^2}{2y}=\frac{x+y+2x^3}{2y}\)
tớ nghĩ tớ làm sai rồi
sorry bn nha :<
lần sau nếu chắc 100% t mói tl
rút gọn
a,\(\frac{8x^2y^3}{4xy^5}\)
b, \(\frac{-2(x^2y)^6}{(y^6x)^2}\)
c,\(\frac{(x+1)^2}{(x-1)\times(x+1)}\)
\(\frac{8x^2y^3}{4xy^5}=\frac{2x}{y^2}\)
Rút gọn: \(\frac{2x^2-4xy}{x^2+4xy+4y^2}:\frac{4y^2-x^2}{x^2-4xy+4y^2}:\frac{5x^2y-10xy^2}{x^3+6x^2y+12xy^2+8y^3}\)
\(=\frac{2x\left(x-2y\right)}{\left(x+2y\right)^2}:\frac{\left(2y-x\right)\left(2y+x\right)}{\left(x-2y\right)^2}:\frac{5xy\left(x-2y\right)}{\left(x+2y\right)^3}\)
Điều kiện: \(x\ne2y;x\ne-2y;x\ne0;y\ne0\)
\(=\frac{2x\left(x-2y\right)}{\left(x+2y\right)^2}:\frac{\left(2y+x\right)}{\left(x-2y\right)}:\frac{5xy\left(x-2y\right)}{\left(x+2y\right)^3}\)
\(=\frac{2x\left(x-2y\right)}{\left(x+2y\right)^2}\times\frac{x-2y}{x+2y}\times\frac{\left(x+2y\right)^3}{5xy\left(x-2y\right)}=\frac{2\left(x-2y\right)}{5y}\)
1, Thực hiện tính cộng, trừ, nhân, chia các phân thức sau:
a,\(\frac{2x-7}{10x-4}-\frac{3x+5}{4-10x}\)
b,\(\frac{2x+3}{4x^2y^2}:\frac{6x+9}{10x^2y}\)
c,\(\frac{x^2-y^2}{6x^2y^2}:\frac{x+y}{3xy}\)
d,\(\left(\frac{3x}{1-3x}+\frac{2x}{3x+1}\right):\frac{6x^2+10x}{1-6x+9x^2}\)
a) \(\frac{2x-7}{10x-4}-\frac{3x+5}{4-10x}\)
\(=\frac{2x-7}{10x-4}-\frac{-\left(3x+5\right)}{-\left(4-10x\right)}\)
\(=\frac{2x-7}{10x-4}-\frac{5-3x}{10x-4}\)
\(=\frac{2x-7-\left(5-3x\right)}{10x-4}\)
\(=\frac{2x-7-5+3x}{10x-4}\)
\(=\frac{5x-12}{10x-4}\)
Rút gọn: \(\frac{2x^2-4xy}{x^2+4xy+4y^2}:\frac{4y^2-x^2}{x^2-4xy+4y^2}:\frac{5x^2y-10xy^2}{x^3+6x^2y+12xy^2+8y^3}\)
\(=\dfrac{2x\left(x-2y\right)}{\left(x+2y\right)^2}\cdot\dfrac{\left(x-2y\right)^2}{-\left(x-2y\right)\left(x+2y\right)}:\dfrac{5x^2y-10xy^2}{x^3+6x^2y+12xy^3+8y^3}\)
\(=\dfrac{-2x\left(x-2y\right)^2}{\left(x+2y\right)^3}\cdot\dfrac{\left(x+2y\right)^3}{5xy\left(x-2y\right)}\)
\(=\dfrac{-2x\cdot\left(x-2y\right)}{5xy}=\dfrac{-2\left(x-2y\right)}{5y}\)
Rút gọn các phân thức sau
a,\(\frac{2x+2y+5x+5y}{2x+2y-5x-5y}\left(x\ne-y\right)\)
b,\(\frac{4x^2-4xy}{5x^3-5x^2y}\left(x\ne0,x\ne y\right)\)
ai làm đc 3 tick
ko ghi đề bài nha làm luôn
a) \(\frac{\left(2x+2y\right)+\left(5x+5y\right)}{\left(2x+2y\right)-\left(5x+5y\right)}=\frac{2\left(x+y\right)+5\left(x+y\right)}{2\left(x+y\right)-5\left(x+y\right)}=\frac{\left(2+5\right)\left(x+y\right)}{\left(2-5\right)\left(x+y\right)}=\frac{-7}{3}\)
b)\(\frac{4x\left(x-y\right)}{5x^2\left(x-y\right)}=\frac{4x}{5x^2}=\frac{4}{5x}\)
a)ĐK: \(x\ne-y;x,y\ne0\)
\(\frac{2x+2y+5x+5y}{2x+2y-5x-5y}=\frac{2\left(x+y\right)+5\left(x+y\right)}{2\left(x+y\right)-5\left(x+y\right)}\)
\(=\frac{\left(x+y\right)\left(2+5\right)}{\left(x+y\right)\left(2-5\right)}=-\frac{7}{3}\)
b) ĐK: ...bạn tự xét...
\(\frac{4x^2-4xy}{5x^3-5x^2y}=\frac{4x\left(x-y\right)}{5x^2\left(x-y\right)}=\frac{4x}{5x^2}=\frac{4}{5x}\)
Vậy ...
Giải hệ phương trình:
\(\hept{\begin{cases}x^2y+2y+x=4xy\\\frac{1}{x^2}+\frac{1}{xy}+\frac{x}{y}=3\end{cases}}\)