Rút gọn: \(\left(\frac{1}{x^2-xy}-\frac{3y^2}{x^4-xy^3}-\frac{y}{x^3+x^2y+xy^2}\right):\frac{x+y}{x^2+xy+y^2}\)
Rút gọn : \(\left(\frac{1}{x^2-xy}-\frac{3y^2}{x^4-xy^3}-\frac{9}{x^3+x^2y+xy^2}\right).\left(y+\frac{x^2}{x+y}\right)\)
\(\left(\frac{1}{x^2-xy}-\frac{3y^2}{x^4-xy^3}-\frac{9}{x^3+x^2y+xy^2}\right).\left(y+\frac{x^2}{x+y}\right)\)
\(=\left(\frac{1}{x.\left(x-y\right)}-\frac{3y^2}{x.\left(x^3-y^3\right)}-\frac{9}{x.\left(x^2+xy+y^2\right)}\right).\left(\frac{y.\left(x+y\right)}{x+y}+\frac{x^2}{x+y}\right)\)
\(=\left(\frac{1}{x.\left(x-y\right)}-\frac{3y^2}{x.\left(x-y\right)\left(x^2+xy+y^2\right)}-\frac{9}{x.\left(x^2+xy+y^2\right)}\right).\left(\frac{y^2+xy}{x+y}+\frac{x^2}{x+y}\right)\)
\(=\left(\frac{x^2+xy+y^2}{x.\left(x-y\right)\left(x^2+xy+y^2\right)}-\frac{3y^2}{x.\left(x-y\right)\left(x^2+xy+y^2\right)}-\frac{9x-9y}{x.\left(x-y\right)\left(x^2+xy+y^2\right)}\right).\left(\frac{x^2+xy+y^2}{x+y}\right)\)
\(=\frac{x^2+xy-2y^2-9x+9y}{x.\left(x-y\right)\left(x^2+xy+y^2\right)}.\frac{x^2+xy+y^2}{x+y}\)
làm tip nha bận rồi
Rút gọn rồi tính giá trị của biểu thức khi x=1;y=\(-3\frac{1}{4}\)
\(\frac{\left(x-y\right)^2+xy}{\left(x+y\right)^2-xy}\)\(\left[1:\frac{x^5+y^5+x^3y^2+x^2y^3}{\left(x^3y^3\right)\left(x^3+y^3+x^2y+xy^2\right)}\right]\)
Rút gọn rồi tính giá trị của biểu thức tại \(x=\frac{1}{2};y=\frac{1}{3}\)
\(A=\left(\frac{4}{x-y}-\frac{x-y}{y^2}\right).\frac{y^2-xy}{x-3y}+\left(\frac{x}{2}-\frac{x^2-xy}{x-2y}\right):\frac{xy+y^2}{2x-4y}\)
\(A=\left(\frac{4}{x-y}-\frac{x-y}{y^2}\right).\frac{y^2-xy}{x-3y}+\left(\frac{x}{2}-\frac{x^2-xy}{x-2y}\right):\frac{xy+y^2}{2x-4y}\)
\(=\frac{4y^2-\left(x-y\right)^2}{y^2\left(x-y\right)}.\frac{y^2-xy}{x-3y}+\frac{x\left(x-2y\right)-2\left(x^2-xy\right)}{2\left(x-2y\right)}.\frac{2x-4y}{xy+y^2}\)
\(=\frac{3y^2+2xy-x^2}{y^2\left(x-y\right)}.\frac{y^2-xy}{x-3y}+\frac{-x^2}{2\left(x-2y\right)}.\frac{2x-4y}{xy+y^2}\)
\(=\frac{\left(x+y\right)\left(3y-x\right)}{y^2\left(x-y\right)}.\frac{y\left(y-x\right)}{x-3y}-\frac{x^2}{2\left(x-2y\right)}.\frac{2\left(x-2y\right)}{y\left(x+y\right)}\)
\(=\frac{\left(x+y\right)}{y}-\frac{x^2}{y\left(x+y\right)}\)
\(=\frac{\left(x+y\right)^2-x^2}{y\left(x+y\right)}=\frac{2xy+y^2}{y\left(x+y\right)}=\frac{2x+y}{x+y}\)
Giờ chỉ cần thế x, y vô nữa là xong nhé.
\(A=\left(\frac{4}{x-y}-\frac{x-y}{y^2}\right).\frac{y^2-xy}{x-3y}\)\(+\left(\frac{x}{2}-\frac{x^2-xy}{x-2y}\right):\frac{xy+y^2}{2x-4y}\)
\(=\left(\frac{4}{x-y}-\frac{x-y}{y^2}\right).\frac{y\left(y-x\right)}{x-3y}\)\(+\left(\frac{x}{2}-\frac{x\left(x-y\right)}{x-2y}\right):\frac{y\left(x+y\right)}{2\left(x-2y\right)}\)
\(=\frac{4y\left(y-x\right)}{\left(x-y\right)\left(x-3y\right)}-\frac{\left(x-y\right)y\left(y-x\right)}{y^2\left(x-3y\right)}\)\(+\frac{x.2\left(x-2y\right)}{2.y\left(x+y\right)}-\frac{x\left(x-y\right).2\left(x-2y\right)}{\left(x-2y\right).y\left(x+y\right)}\)
\(=\frac{-4y}{x-3y}+\frac{\left(x-y\right)^2}{y\left(x-3y\right)}+\frac{x\left(x-2y\right)}{y\left(x+y\right)}-\frac{2x\left(x-y\right)}{y\left(x+y\right)}\)
\(=\frac{-4y^2+x^2-2xy+y^2}{y\left(x-3y\right)}+\frac{x^2-2xy-2x^2+2xy}{y\left(x+y\right)}\)
\(=\frac{x^2-2xy-3y^2}{y\left(x-3y\right)}+\frac{-x^2}{y\left(x+y\right)}\)
\(=\frac{x^2+xy-3xy-3y^2}{y\left(x-3y\right)}-\frac{x^2}{y\left(x+y\right)}\)
\(=\frac{x\left(x+y\right)-3y\left(x+y\right)}{y\left(x-3y\right)}-\frac{x^2}{y\left(x+y\right)}\)
\(\frac{\left(x+y\right)\left(x-3y\right)}{y\left(x-3y\right)}-\frac{x^2}{y\left(x+y\right)}\)
\(=\frac{x+y}{y}-\frac{x^2}{y\left(x+y\right)}=\frac{\left(x+y\right)^2-x^2}{y\left(x+y\right)}\)
\(=\frac{x^2-2xy+y^2-x^2}{y\left(x+y\right)}=\frac{-2xy+y^2}{y\left(x+y\right)}\)
\(=\frac{y\left(y-2x\right)}{y\left(x+y\right)}=\frac{y-2x}{x+y}\)
Thay \(x=\frac{1}{2};y=\frac{1}{3}\)vào A ta có :
\(A=\frac{\frac{1}{3}-2.\frac{1}{2}}{\frac{1}{2}+\frac{1}{3}}=\frac{\frac{1}{3}-1}{\frac{3}{6}+\frac{2}{6}}=\frac{2}{3}:\frac{5}{6}=\frac{2.6}{3.5}=\frac{4}{5}\)
Vậy \(A=\frac{4}{5}\)tại \(x=\frac{1}{2};y=\frac{1}{3}\)
Ừ nhở chị sai từ chỗ \(\frac{\left(x+y\right)^2-x^2}{y\left(x+y\right)}=\frac{x^2+2xy+y^2-x^2}{y\left(x+y\right)}=\frac{y^2+2xy}{y\left(x+y\right)}\)em nhé
Bài 1: Thu gọn
a) \(\frac{1}{5}x^4y^3-3x^4y^3\)
b) \(5x^2y^5-\frac{1}{4}x^2y^5\)
c) \(\frac{1}{7}x^2y^3.\left(-\frac{14}{3}xy^2\right)-\frac{1}{2}xy.\left(x^2y^{\text{4}}\right)\)
d) \(\left(3xy\right)^2.\left(-\frac{1}{2}x^3y^2\right)\)
e) \(-\frac{1}{4}xy^2+\frac{2}{5}x^2y+\frac{1}{2}xy^2-x^2y\)
f) \(\frac{1}{2}x^4y.\left(-\frac{2}{3}x^3y^2\right)-\frac{1}{3}x^7y^3\)
g) \(\frac{1}{2}x^2y.\left(-10x^3yz^2\right).\frac{1}{4}x^5y^3z\)
h) \(4.\left(-\frac{1}{2}x\right)^2-\frac{3}{2}x.\left(-x\right)+\frac{1}{3}x^2\)
i) \(1\frac{2}{3}x^3y.\left(\frac{-1}{2}xy^2\right)^2-\frac{5}{4}.\frac{8}{15}x^3y.\left(-\frac{1}{2}xy^2\right)^2\)
k) \(-\frac{3}{2}xy^2.\left(\frac{3}{4}x^2y\right)^2-\frac{3}{5}xy.\left(-\frac{1}{3}x^4y^3\right)+\left(-x^2y\right)^2.\left(xy\right)^2\)
n) \(-2\frac{1}{5}xy.\left(-5x\right)^2+\frac{3}{4}y.\frac{2}{3}\left(-x^3\right)-\frac{1}{9}.\left(-x\right)^3.\frac{1}{3}y\)
m) \(\left(-\frac{1}{3}xy^2\right)^2.\left(3x^2y\right)^3.\left(-\frac{5}{2}xy^2z^3\right)^{^2}\)
p) \(-2y.\left|2\right|x^4y^5.\left|-\frac{3}{4}\right|x^3y^2z\)
Bài 1:
a) \(\frac{1}{5}x^4y^3-3x^4y^3\)
= \(\left(\frac{1}{5}-3\right)x^4y^3\)
= \(-\frac{14}{5}x^4y^3.\)
b) \(5x^2y^5-\frac{1}{4}x^2y^5\)
= \(\left(5-\frac{1}{4}\right)x^2y^5\)
= \(\frac{19}{4}x^2y^5.\)
Mình chỉ làm 2 câu thôi nhé, bạn đăng nhiều quá.
Chúc bạn học tốt!
Rút gọn biểu thức
A= \(1+\left[\frac{2x^3y^2+2x^2y^3}{x+y}:\left(\frac{2x^2y^2}{x^2+xy}+\frac{2x^2y^2}{y^2+xy}\right)\right]\)
Rút gọn : \(\left(\frac{1}{x^2-xy}-\frac{3y^2}{x^4-xy^3}-\frac{y}{x^3+x^2y+xy^2}\right)\left(y+\frac{x^2}{x+y}\right)\)
=\(\left(\frac{1}{x\left(x-y\right)}-\frac{3y^2}{x\left(x-y\right)\left(x^2+xy+y^2\right)}-\frac{y}{x\left(x^2+xy+y^2\right)}\right)\)\(\left(\frac{y\left(x+y\right)+x^2}{x+y}\right)\)
=\(\left(\frac{x^2+xy+y^2-3y^2-y\left(x-y\right)}{x\left(x-y\right)\left(x^2+xy+y^2\right)}\right)\) \(\left(\frac{x^2+xy+y^2}{x+y}\right)\)
=\(\left(\frac{x^2+xy-2y^2-xy+y^2}{x\left(x-y\right)}\right)\left(\frac{1}{x+y}\right)\)
=\(\frac{x^2-y^2}{x\left(x-y\right)\left(x+y\right)}\)=\(\frac{\left(x-y\right)\left(x+y\right)}{x\left(x-y\right)\left(x+y\right)}\) =\(\frac{1}{x}\)
Rút gọn
\(\left(\frac{x-y}{2y-x}-\frac{x^2+y^2+y-2}{x^2-xy-2y^2}\right):\left(\frac{x^4+4x^2y^2+y^4-4}{x^2+y+xy+x}\right):\frac{1}{2x^2+y+z}\)
35Cho biểu thức
P=\(\left[\left(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}\right)\frac{2}{\sqrt{x}+\sqrt{y}}+\frac{1}{x}+\frac{1}{y}\right]:\frac{\sqrt{x^3}+y\sqrt{x}+x\sqrt{y}+\sqrt{y^3}}{\sqrt{xy^3}+\sqrt{x^3y}}\)
a) Rút gọn P
b)Cho xy=16 . Tìm Min P
34 Cho biểu thức
P=\(\frac{x}{\sqrt{xy}-2y}-\frac{2\sqrt{x}}{x+\sqrt{x}-2\sqrt{xy}-2\sqrt{y}}-\frac{1-x}{1-\sqrt{x}}\)
a) Rút gọn P
b)Tính P biết 2x^2+y^2-4x-2xy+4=0
cho BIỂU THỨC:
P =\(\left[\left(\frac{x-y}{2y-x}-\frac{x^2+y^2+y-2}{x^2-xy-2y^2}\right):\frac{4x^4+4x^2y+y^2-4}{x^2+y+xy+x}\right]:\frac{x+1}{2x^2y+2}\)
RÚT GỌN P