BÀI 6 rút gọn phân thức
\(\dfrac{2(x+1)^{2}}{4x(x+1)}\)
\(\dfrac{(8-x)(-x-2)}{(x+2)^{2}}\)
\(\dfrac{2(x-y)}{y-x} \)
\(\dfrac{(x+2)^{2}}{2x+4}\)
BÀI 6 :rút gọn phân thức
\(\dfrac{x^3+3x^3+3x+1}{x^2+x}\)
b)\(\dfrac{x^3-3x^2+3x-1}{2x-2}\)
c)\(\dfrac{x^2+4x+4}{2x+4}\)
d)\(\dfrac{(x-1)(-x-2)}{x+2}\)
e)\(\dfrac{x^2-y^2}{x+y}\)
f)\(\dfrac{3x^2+4xy^2}{6x+8y}\)
g)\(\dfrac{-3x^2-6x}{4-x^2}\)
BÀI 7 :quy đồng mẫu thức các phân thức
\(\dfrac{2}{5x^3y^2}và \dfrac{3}{4xy}\)
b)\(\dfrac{x}{x^2-2xy+y^2} và \dfrac{x}{x^2-xy}\)
c)\(\dfrac{1}{x+2};\dfrac{2}{2x+4}và \dfrac{3}{3x+6}\)
d)\(\dfrac{1}{x+3};\dfrac{2}{2x-6}và \dfrac{3}{3x-9}\)
6:
a: ĐKXĐ: x<>0
\(\dfrac{x^3+3x^2+3x+1}{x^2+x}\)
\(=\dfrac{\left(x+1\right)^3}{x\left(x+1\right)}=\dfrac{\left(x+1\right)^2}{x}\)
b: ĐKXĐ: x<>1
\(\dfrac{x^3-3x^2+3x-1}{2x-2}\)
\(=\dfrac{\left(x-1\right)^3}{2\left(x-1\right)}=\dfrac{\left(x-1\right)^2}{2}\)
c: ĐKXĐ: x<>-2
\(\dfrac{x^2+4x+4}{2x+4}\)
\(=\dfrac{\left(x+2\right)^2}{2\left(x+2\right)}\)
\(=\dfrac{x+2}{2}\)
d: ĐKXĐ: x<>-2
\(\dfrac{\left(x-1\right)\left(-x-2\right)}{x+2}\)
\(=\dfrac{\left(-x+1\right)\left(x+2\right)}{x+2}=-x+1\)
e: ĐKXĐ: x<>-y
\(\dfrac{x^2-y^2}{x+y}=\dfrac{\left(x-y\right)\left(x+y\right)}{x+y}=x-y\)
g: ĐKXĐ: \(x\notin\left\{2;-2\right\}\)
\(\dfrac{-3x^2-6x}{4-x^2}=\dfrac{3x^2+6x}{x^2-4}\)
\(=\dfrac{3x\left(x+2\right)}{\left(x+2\right)\cdot\left(x-2\right)}=\dfrac{3x}{x-2}\)
7:
a: \(\dfrac{2}{5x^3y^2}=\dfrac{2\cdot4}{20x^3y^2}=\dfrac{8}{20x^3y^2}\)
\(\dfrac{3}{4xy}=\dfrac{3\cdot5\cdot x^2y}{20x^3y^2}=\dfrac{15x^2y}{20x^3y^2}\)
b: \(\dfrac{x}{x^2-2xy+y^2}=\dfrac{x}{\left(x-y\right)^2}\)
\(\dfrac{x}{x^2-xy}=\dfrac{x}{x\left(x-y\right)}=\dfrac{1}{x-y}=\dfrac{\left(x-y\right)}{\left(x-y\right)^2}\)
c: \(\dfrac{1}{x+2}=\dfrac{6}{6\left(x+2\right)}\)
\(\dfrac{2}{2x+4}=\dfrac{2}{2\left(x+2\right)}=\dfrac{1}{x+2}=\dfrac{6}{6\left(x+2\right)}\)
\(\dfrac{3}{3x+6}=\dfrac{3}{3\left(x+2\right)}=\dfrac{6}{6\left(x+2\right)}\)
d:
\(\dfrac{2}{2x-6}=\dfrac{2}{2\left(x-3\right)}=\dfrac{1}{x-3};\dfrac{3}{3x-9}=\dfrac{3}{3\left(x-3\right)}=\dfrac{1}{x-3}\)
\(\dfrac{2}{2x-6}=\dfrac{1}{x-3}=\dfrac{x+3}{\left(x-3\right)\left(x+3\right)}\)
\(\dfrac{3}{3x-9}=\dfrac{1}{x-3}=\dfrac{x+3}{\left(x-3\right)\left(x+3\right)}\)
\(\dfrac{1}{x+3}=\dfrac{x-3}{\left(x+3\right)\left(x-3\right)}\)
Bài 1: Rút gọn các phân thức sau:
a) \(\dfrac{x^3-1}{x^2+x+1}\)
b) \(\dfrac{x^2+2xy+y^2}{2x^2+xy-y^2}\)
c) \(\dfrac{ax^4-a^4x}{a^2+ax+x^2}\)
d) \(\dfrac{x^3+x^2-6x}{x^3-4x}\)
e) \(\dfrac{2x^2+xy-y^2}{2x^2-3xy+y^2}\)
Mng giúp e với ạ.E đg cần gấp có trc trưa mai đc ko ạ:)))
E cảm ơn ạ!!!
a) \(\dfrac{x^3-1}{x^2+x+1}=\dfrac{\left(x-1\right)\left(x^2+x+1\right)}{x^2+x+1}=x-1\)
b) \(\dfrac{x^2+2xy+y^2}{2x^2+xy-y^2}\)
\(=\dfrac{\left(x+y\right)^2}{x^2+xy+x^2-y^2}=\dfrac{\left(x+y\right)^2}{x\left(x+y\right)+\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{\left(x+y\right)^2}{\left(2x-y\right)\left(x+y\right)}=\dfrac{x+y}{\left(2x-y\right)}\)
c) \(\dfrac{ax^4-a^4x}{a^2+ax+x^2}\)
\(=\dfrac{ax\left(x^3-a^3\right)}{a^2+ax+x^2}\)
\(=\dfrac{ax\left(x-a\right)\left(a^2+ax+x^2\right)}{a^2+ax+x^2}\)
\(=ax\left(x-a\right)\)
Rút gọn các phân thức sau:
a) \(\dfrac{5x}{10}\)
b)\(\dfrac{4xy}{2y}\) (y≠0)
c)\(\dfrac{5x-5y}{3x-3y}\) (x≠y)
d) \(\dfrac{x^2-y^2}{x+y}\)(chưa có điều kiện xác định)
e) \(\dfrac{x^3-x^2+x-1}{x^2-1}\)(chưa có điều kiện xác định)
f) \(\dfrac{x^2+4x+4}{2x+4}\)(chưa có điều kiện xác định)
a) \(\dfrac{5x}{10}=\dfrac{x}{2}\)
b) \(\dfrac{4xy}{2y}=2x\left(y\ne0\right)\)
c) \(\dfrac{5x-5y}{3x-3y}=\dfrac{5}{3}\left(x\ne y\right)\)
d) \(\dfrac{x^2-y^2}{x+y}=x-y\left(đk:x\ne-y\right)\)
e) \(\dfrac{x^3-x^2+x-1}{x^2-1}=\dfrac{x^2+1}{x+1}\left(đk:x\ne\pm1\right)\)
f) \(\dfrac{x^2+4x+4}{2x+4}=\dfrac{x+2}{2}\left(đk:x\ne-2\right)\)
rút gọn phân thức:
\(\dfrac{x^3-4x^2+4x}{x^2-4}\)
\(\dfrac{x^2y+2xy^2+y^3}{2x^2+xy-y^2}\)
1. \(\dfrac{x^3-4x^2+4x}{x^2-4}=\dfrac{x\left(x^2-4x+4\right)}{\left(x+2\right)\left(x-2\right)}=\dfrac{x\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)}=\dfrac{x\left(x-2\right)}{x+2}\)
\(\dfrac{x^2y+2xy^2+y^3}{2x^2+xy-y^2}=\dfrac{y\left(x^2+2xy+y^2\right)}{2x^2+2xy-xy-y^2}=\dfrac{y\left(x+y\right)^2}{2x\left(x+y\right)-y\left(x+y\right)}\)
\(=\dfrac{y\left(x+y\right)^2}{\left(2x-y\right)\left(x+y\right)}=\dfrac{y\left(x+y\right)}{2x-y}\)
bài 11.rút gọn biểu thức:
\(a,\dfrac{9x^2}{11y^2}:\dfrac{3x}{2y}:\dfrac{6x}{11y}\) \(b,\dfrac{3x+15y}{x^3-y^3}:\dfrac{x+5y}{x-y}\)
\(c,\dfrac{x^2-1}{x^2-4x+4}:\dfrac{x+1}{2-x}\) \(d,\dfrac{5x+10}{x+2}:\dfrac{5y}{x}\)
\(e,\dfrac{2x}{3x-3y}:\dfrac{x^2}{x-y}\) \(f,\dfrac{5x-3}{4x^2y}-\dfrac{x-3}{4x^2y}\)
\(g,\dfrac{3x+10}{x+3}-\dfrac{x+4}{x+3}\) \(h,\dfrac{4}{x-1}+\dfrac{2}{1-x}+\dfrac{x}{x-1}\)
\(i,\dfrac{2x^2-x}{x-1}+\dfrac{x+1}{1-x}+\dfrac{2-x^2}{x-1}\) \(j,\dfrac{x-2}{x-6}-\dfrac{x-18}{6-x}+\dfrac{x+2}{x-6}\)
\(k,\dfrac{x}{x^2-4}+\dfrac{2}{2-x}+\dfrac{1}{x+2}\) \(m,\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}\)
\(n,\dfrac{3}{x+3}-\dfrac{x-6}{x^2+3x}\) \(p,\dfrac{x+3}{x}-\dfrac{x}{x-3}+\dfrac{9}{x^2-3x}\)
f: \(=\dfrac{5x-3-x+3}{4x^2y}=\dfrac{4x}{4x^2y}=\dfrac{1}{xy}\)
g: \(=\dfrac{3x+10-x-4}{x+3}=\dfrac{2x+6}{x+3}=2\)
h: \(=\dfrac{4-2+x}{x-1}=\dfrac{x+2}{x-1}\)
n: \(=\dfrac{3x-x+6}{x\left(x+3\right)}=\dfrac{2\left(x+3\right)}{x\left(x+3\right)}=\dfrac{2}{x}\)
p: \(=\dfrac{x^2-9-x^2+9}{x\left(x-3\right)}=0\)
k: \(=\dfrac{x-2x-4+x-2}{\left(x+2\right)\left(x-2\right)}=\dfrac{-6}{x^2-4}\)
m: \(=\dfrac{3x-x+6}{x\left(2x+6\right)}=\dfrac{2x+6}{x\left(2x+6\right)}=\dfrac{1}{x}\)
BÀI 6
\(A=\dfrac{x+15}{x^2-9}-\dfrac{2}{x+3}\)
a) viết điều kiện xác định của biểu thức A
b)rút gọn phân thức
c)tìm giá trị của Akhi x=-1
BÀI 7
\(A=\dfrac{x+2}{x-2}+\dfrac{x-1}{x+2}\dfrac{x^2-4x}{4-x^2}\)với x2-4≠0
a)rút gọn biểu thức A
b)tính giá trị cua A khi x=4
a) ĐKXĐ:
\(\left\{{}\begin{matrix}x^2-9\ne0\\x+3\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\pm3\\x\ne-3\end{matrix}\right.\Leftrightarrow x\ne\pm3\)
b) \(A=\dfrac{x+15}{x^2-9}-\dfrac{2}{x+3}\)
\(A=\dfrac{x+15}{\left(x+3\right)\left(x-3\right)}-\dfrac{2\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}\)
\(A=\dfrac{x+15-2x+6}{\left(x+3\right)\left(x-3\right)}\)
\(A=\dfrac{21-x}{\left(x+3\right)\left(x-3\right)}\)
c) Thay x = - 1 vào A ta có:
\(A=\dfrac{21-\left(-1\right)}{\left(-1+3\right)\left(-1-3\right)}=\dfrac{21+1}{2\cdot-4}=\dfrac{22}{-8}=-\dfrac{11}{4}\)
Cho biểu thức
(\(\dfrac{x^2-2x}{2x^2+8}\) - \(\dfrac{2x^2}{8-4x+2x^2-x^3}\)).(1-\(\dfrac{1}{x}\)-\(\dfrac{2}{x^2}\))(x≠0;x≠2)
rút gọn biểu thức
tính giá trị biểu thức với x1/2
cho biểu thức
P=(\(\dfrac{x^2-2x}{2x^2+8}-\dfrac{2x^2}{8-4x+2x^2-x^3}\)).(1-\(\dfrac{1}{x}-\dfrac{2}{x^2}\)) ( x≠0; x≠2)
rút gọn biểu thức P
tính giá trị biểu thức P với x=1/2
a) Ta có: \(P=\left(\dfrac{x^2-2x}{2x^2+8}-\dfrac{2x^2}{8-4x+2x^2-x^3}\right)\cdot\left(1-\dfrac{1}{x}-\dfrac{2}{x^2}\right)\)
\(=\left(\dfrac{x\left(x-2\right)}{2\left(x^2+4\right)}+\dfrac{2x^2}{\left(x-2\right)\left(x^2+4\right)}\right)\cdot\left(\dfrac{x^2-x-2}{x^2}\right)\)
\(=\dfrac{x\left(x-2\right)^2+4x^2}{2\left(x-2\right)\left(x^2+4\right)}\cdot\dfrac{\left(x^2-x-2\right)}{x^2}\)
\(=\dfrac{x\left[x^2-4x+4+4x\right]}{2\left(x-2\right)\left(x^2+4\right)}\cdot\dfrac{x^2-x-2}{x^2}\)
\(=\dfrac{x\left(x^2+4\right)}{2\left(x-2\right)\left(x^2+4\right)}\cdot\dfrac{\left(x-2\right)\left(x+1\right)}{x^2}\)
\(=\dfrac{x+1}{2x}\)
b) Thay \(x=\dfrac{1}{2}\) vào P, ta được:
\(P=\dfrac{1}{2}+1=\dfrac{3}{2}\)
Rút gọn các biểu thức:
a) {\(\dfrac{1}{x^2}\) + \(\dfrac{1}{y^2}\) + \(\dfrac{2}{x+y}\)(\(\dfrac{1}{x}\) + \(\dfrac{1}{y}\))} : \(\dfrac{x^3+y^3}{x^2y^2}\)
b) {\(\dfrac{1}{\left(2x-y\right)^2}\) + \(\dfrac{2}{4x^2-y^2}\) + \(\dfrac{1}{\left(2x+y\right)^2}\)} . \(\dfrac{4x^2+4xy+y^2}{16x}\)
c) (\(\dfrac{x^2-xy}{x^2y+y^3}\) - \(\dfrac{2x^2}{y^3-xy^2+x^2y-x^3}\))(1 - \(\dfrac{y-1}{x}\) - \(\dfrac{y}{x^2}\))