\(a)\frac{1}{x+3}+\frac{x}{x^2-6x+9}\)
\(b)\frac{2x}{x^2-9}-\frac{x-1}{x+3}\)
\(c)\frac{2x+1}{x-2}.\frac{2-x}{2x+1}\)
Tính
Những câu hỏi liên quan
quy đồng phân thức
b) \(\frac{x}{x^3-27};\frac{2x}{x^2-6x+9};\frac{1}{x^2+3x+9}\)
c) \(\frac{x-1}{2x+2};\frac{x+1}{2x-2};\frac{1}{1-x^2}\)
d)\(\frac{1}{x^3+1};\frac{3}{2x+2};\frac{2}{x^2-x+1}\)
\(MTC:\left(x-3\right)^2\left(x^2+3x+9\right)\)
\(\frac{x}{x^3-27}=\frac{x}{\left(x-3\right)\left(x^2+3x+9\right)}=\frac{x\left(x-3\right)}{\left(x-3\right)^2\left(x^2+3x+9\right)}\)
\(\frac{2x}{x^2-6x+9}=\frac{2x}{\left(x-3\right)^2}=\frac{2x\left(x^2+3x+9\right)}{\left(x-3\right)^2\left(x^2+3x+9\right)}\)
\(\frac{1}{x^2+3x+9}=\frac{\left(x-3\right)^2}{\left(x-3\right)^2\left(x^2+3x+9\right)}\)
\(MTC:2\left(x-1\right)\left(x+1\right)\)
\(\frac{x-1}{2x+2}=\frac{x-1}{2\left(x+1\right)}=\frac{\left(x-1\right)^2}{2\left(x-1\right)\left(x+1\right)}\)
\(\frac{x+1}{2x-2}=\frac{x+1}{2\left(x-1\right)}=\frac{\left(x+1\right)^2}{2\left(x-1\right)\left(x+1\right)}\)
\(\frac{1}{1-x^2}=-\frac{1}{\left(x-1\right)\left(x+1\right)}=-\frac{2}{2\left(x-1\right)\left(x+1\right)}\)
\(MTC:2\left(x+1\right)\left(x^2-x+1\right)\)
\(\frac{1}{x^3+1}=\frac{1}{\left(x+1\right)\left(x^2-x+1\right)}=\frac{2}{2\left(x+1\right)\left(x^2-x+1\right)}\)
\(\frac{3}{2x+2}=\frac{3}{2\left(x+1\right)}=\frac{3\left(x^2-x+1\right)}{2\left(x+1\right)\left(x^2-x+1\right)}\)
\(\frac{2}{x^2-x+1}=\frac{4\left(x+1\right)}{2\left(x+1\right)\left(x^2-x+1\right)}\)
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1. Thực hiện phép tính:
a) \(\frac{1-3x}{2x}+\frac{3x-2}{2x-1}+\frac{3x-2}{2x-4}\)
b) \(\frac{1}{x^2+6x+y}+\frac{1}{6x-x^2-9}+\frac{x}{x^2-9}\)
c) \(\frac{x^2+2}{x^3-1}+\frac{2}{x^2+x+1}+\frac{1}{1-x}\)
d) \(\frac{x}{x-2y}+\frac{x}{x+2y}+\frac{4xy}{4y^2-x^2}\)
a)có khả năng sai đề bài
b)Liệu có sai đề bài không
c)\(=\frac{x^2+2}{\left(x-1\right)\left(x^2+x+1\right)}+\frac{2\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}+\frac{-\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)(phân số cuối có âm vì (1-x)=-(x-1)
\(=\frac{x^2+2+2x-2-x^2-x-1}{\left(x-1\right)\left(x^2+x+1\right)}\)(Hơi tắt)
\(=\frac{x-1}{\left(x-1\right)\left(x^2+x+1\right)}=\frac{1}{x^2+x+1}\)
d)\(=\frac{x\left(x+2y\right)}{\left(x-2y\right)\left(x+2y\right)}+\frac{x\left(x-2y\right)}{\left(x-2y\right)\left(x+2y\right)}+\frac{4xy}{\left(x-2y\right)\left(x+2y\right)}\)
\(=\frac{x^2+2xy+x^2-2xy+4xy}{\left(x-2y\right)\left(x+2y\right)}\)
\(=\frac{2x^2+4xy}{\left(x-2y\right)\left(x+2y\right)}=\frac{2x\left(x+2y\right)}{\left(x-2y\right)\left(x+2y\right)}=\frac{2x}{x-2y}\)
1) Giải các phương trình:a) frac{x-3}{5}-frac{2x-1}{10}frac{x+1}{2}+frac{1}{4}b)frac{x+3}{2}-frac{2-1}{3}-1frac{x+5}{6}c)frac{x-1}{4}-frac{5-2x}{9}3x-frac{2}{3}d)frac{2x-1}{4}+frac{x-3}{3}frac{4x-2}{3}-frac{6x+7}{12}e)frac{3x-2}{5}+frac{x-1}{9}frac{14x-3}{15}-frac{2x+1}{9}
Đọc tiếp
1) Giải các phương trình:
a) \(\frac{x-3}{5}-\frac{2x-1}{10}=\frac{x+1}{2}+\frac{1}{4}\)
b)\(\frac{x+3}{2}-\frac{2-1}{3}-1=\frac{x+5}{6}\)
c)\(\frac{x-1}{4}-\frac{5-2x}{9}=3x-\frac{2}{3}\)
d)\(\frac{2x-1}{4}+\frac{x-3}{3}=\frac{4x-2}{3}-\frac{6x+7}{12}\)
e)\(\frac{3x-2}{5}+\frac{x-1}{9}=\frac{14x-3}{15}-\frac{2x+1}{9}\)
\(\frac{x-3}{5}-\frac{2x-1}{10}=\frac{x+1}{2}+\frac{1}{4}\)
\(< =>\frac{\left(x-3\right).4}{20}-\frac{\left(2x-1\right).2}{20}=\frac{\left(x+1\right).10}{20}+\frac{5}{20}\)
\(< =>4x-12-4x+2=10x+10+5\)
\(< =>10x=-10-10-5=-25\)
\(< =>x=-\frac{25}{10}=-\frac{5}{2}\)
\(\frac{x+3}{2}-\frac{2x-1}{3}-1=\frac{x+5}{5}\)
\(< =>\frac{\left(x+3\right).15}{30}-\frac{\left(2x-1\right).10}{30}-\frac{30}{30}=\frac{\left(x+5\right).5}{30}\)\(< =>15x+45-20x+10-30=5x+25\)
\(< =>-5x+25=5x+25< =>10x=0< =>x=0\)
\(\frac{x-1}{4}-\frac{5-2x}{9}=3x-\frac{2}{3}\)
\(< =>\frac{\left(x-1\right).9}{36}-\frac{\left(5-2x\right).4}{36}=\frac{3x.36}{36}-\frac{2.12}{36}\)
\(< =>\left(x-1\right).9-\left(5-2x\right).4=108x-24\)
\(< =>9x-9-20+8x=108x-24\)
\(< =>108x-17x=-29+24\)
\(< =>91x=-5< =>x=-\frac{5}{91}\)
Xem thêm câu trả lời
a,\(\frac{1}{2x-2}-\frac{x-1}{3x^2+6x+3}\)
b,\(\frac{4}{x^2-1}+\frac{1}{x+1}+\frac{-2}{x-1}\)
c,\(\frac{5}{2x^2+6x}-\frac{4-3x^2}{x^2-9}-3\)
ai jup em vs
Đề bài yêu cầu gì bạn?
Rút gọn các phân thức đại số sau:Afrac{2x}{x^2-3x}+frac{2x}{x^2-4x+3}+frac{x}{x-1}1Bfrac{x}{x+2}+frac{2}{x-2}-frac{4x}{4-x^2}Cfrac{1+x}{3-x}-frac{1-2x}{3+x}-frac{xleft(1-xright)}{9-x^2}Dfrac{5}{2x^2+6x}-frac{4-3x^2}{x^2-9}-3Efrac{3x+2}{x^2-2x+1}-frac{6}{x^2-1}-frac{3x-2}{x^2+2x+1}Giúp mik mấy câu này vs mik đg cần gấp mik cảm ơn mng trước😘😘
Đọc tiếp
Rút gọn các phân thức đại số sau:
A=\(\frac{2x}{x^2-3x}+\frac{2x}{x^2-4x+3}+\frac{x}{x-1}\)1
B=\(\frac{x}{x+2}+\frac{2}{x-2}-\frac{4x}{4-x^2}\)
C=\(\frac{1+x}{3-x}-\frac{1-2x}{3+x}-\frac{x\left(1-x\right)}{9-x^2}\)
D=\(\frac{5}{2x^2+6x}-\frac{4-3x^2}{x^2-9}-3\)
E=\(\frac{3x+2}{x^2-2x+1}-\frac{6}{x^2-1}-\frac{3x-2}{x^2+2x+1}\)
Giúp mik mấy câu này vs mik đg cần gấp mik cảm ơn mng trước😘😘
Làm ngắn gọn thôi nhé :v
\(A=\frac{2x}{x^2-3x}+\frac{2x}{x^2-4x+3}+\frac{x}{x-1}\)
\(A=\frac{x^5-3x^4-3x^3+11x^2-6x}{x^5-8x^2+22x^2-24x+9}\)
\(A=\frac{x^4-3x^3-3x^2+11x-6}{x^4-8x^3+22x^2-24x+9}\)
\(A=\frac{\left(x-1\right)\left(x-1\right)\left(x+2\right)\left(x-3\right)}{\left(x-1\right)\left(x-1\right)\left(x-3\right)\left(x-3\right)}\)
\(A=\frac{x+2}{x-3}\)
\(B=\frac{x}{x+2}+\frac{2}{x-2}-\frac{4x}{4-x^2}\)
\(B=\frac{-x^4-4x^3+16x+16}{-x^4+8x^2-16}\)
\(B=\frac{\left(-x-2\right)\left(x+2\right)\left(x+2\right)\left(x-2\right)}{\left(-x-2\right)\left(x-2\right)\left(x+2\right)\left(x-2\right)}\)
\(B=\frac{x+2}{x-2}\)
\(C=\frac{1+x}{3-x}-\frac{1-2x}{3+x}-\frac{x\left(1-x\right)}{9-x^2}\)
\(C=\frac{1+x}{3-x}-\left(\frac{1-2x}{3+x}\right)-\frac{x\left(1-x\right)}{9-x^2}\)
\(C=\frac{10x}{-x^2+9}\)
\(D=\frac{5}{2x^2+6x}-\frac{4-3x^2}{x^2-9}-3\)
\(D=\frac{5}{2x^2+6x}-\left(\frac{4-3x^2}{x^2-9}\right)-3\)
\(D=\frac{51x^2+138x-45}{2x^4+6x^2-18x^2-54x}\)
\(D=\frac{3\left(17x-5\right)\left(x+3\right)}{2x\left(x+3\right)\left(x+3\right)\left(x-2\right)}\)
\(D=\frac{51x-15}{2x^3-18x}\)
\(E=\frac{3x+2}{x^2-2x+1}-\frac{6}{x^2-1}-\frac{3x-2}{x^2+2x+1}\)
\(E=\frac{3x+2}{x^2-2x+1}-\frac{6}{x^2-1}-\left(\frac{3x-2}{x^2+2x+1}\right)\)
\(E=\frac{10x^4-10}{x^6-3x^4+3x^2-1}\)
\(E=\frac{10\left(x^2+1\right)\left(x+1\right)\left(x-1\right)}{\left(x+1\right)\left(x+1\right)\left(x+1\right)\left(x-1\right)\left(x-1\right)\left(x-1\right)}\)
\(E=\frac{10x^2+10}{x^4-2x+1}\)
Giải phương trình:
a) \(\frac{x+3}{x-2}-\frac{2x+3}{x+2}=\frac{2x^2+5x+12}{x^2-4}\)
b) \(\frac{2x+5}{x-3}+\frac{x-1}{x+3}=\frac{x^2+6x+18}{x^2-9}\)
a) \(\frac{x+3}{x-2}-\frac{2x+3}{x+2}=\frac{2x^2+5x+12}{x^2-4}\)
ĐKXĐ: \(\left\{\begin{matrix}x\ne2\\x\ne-2\end{matrix}\right.\)
\(\Rightarrow\left(x+3\right)\left(x+2\right)-\left(2x+3\right)\left(x-2\right)=2x^2+5x+12\)
\(\Leftrightarrow x^2+2x+3x+6-2x^2+4x-3x+6-2x^2-5x-12=0\)
\(\Leftrightarrow-3x^2+4x=0\)
\(\Leftrightarrow3x^2-4x=0\)
\(\Leftrightarrow x\left(3x-4\right)=0\)
\(\Leftrightarrow\left[\begin{matrix}x=0\\3x-4=0\end{matrix}\right.\Leftrightarrow\left[\begin{matrix}x=0\\3x=4\end{matrix}\right.\Leftrightarrow\left[\begin{matrix}x=0\left(tmđk\right)\\x=\frac{4}{3}\left(tmđk\right)\end{matrix}\right.\)
Vậy: \(x=0;\frac{4}{3}\)
_Chúc bạn học tốt_
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b) Ta có: \(\frac{2x+5}{x-3}+\frac{x-1}{x+3}=\frac{x^2+6x+18}{x^2-9}\)
ĐKXĐ: \(\left\{\begin{matrix}x\ne3\\x\ne-3\end{matrix}\right.\)
\(\Leftrightarrow\frac{\left(2x+5\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{\left(x-1\right)\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}=\frac{x^2+6x+18}{\left(x+3\right)\left(x-3\right)}\)
\(\Rightarrow\left(2x+5\right)\left(x+3\right)+\left(x-1\right)\left(x-3\right)=x^2+6x-18\)
\(\Leftrightarrow2x^2+6x+5x+15+x^2-3x-x+3-x^2-6x-18=0\)
\(\Leftrightarrow2x^2+x=0\)
\(\Leftrightarrow x\left(2x+1\right)=0\)
\(\Leftrightarrow\left[\begin{matrix}x=0\\2x+1=0\end{matrix}\right.\Leftrightarrow\left[\begin{matrix}x=0\\2x=-1\end{matrix}\right.\Leftrightarrow\left[\begin{matrix}x=0\\x=-\frac{1}{2}\end{matrix}\right.\)
Vậy: \(x=0;-\frac{1}{2}\)
_Chúc bạn học tốt_
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a) x+3/x-2 - 2x+3/x+2 =2x2+5x+12/x2-4
đkxđ : x khác -2; x khác 2
<=>(x+3).(x+2)/(x-2).(x+2) - (2x+3).(x-2)/(x-2).(x+2) = 2x2+5x+12/(x-2).(x+2)
=>x2+2x+3x+6 - 2x2-4x+3x-6 =2x2+5x+12
<=>x2-2x2-2x2 + 2x+3x-4x-5x = 12-6+6
<=>-3x2 - 4x = 0
<=>-x(3x-4)=0
<=>-x=0
<=>3x-4=0
<=>-x=0
<=>3x=4
<=>-x/-1=0/-1
<=>3x/3=4/3
<=>x=0(tm)
<=>x=4/3(tm)
vậy phương trình có nghiệm x=0 ; x=4/3.
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Giải các phương trình
a) \(\frac{2x}{x-1}+\frac{4}{x^2+2x-3}=\frac{2x-5}{x+3}\)
b)\(\frac{x^2-x}{x+3}-\frac{x^2}{x-3}=\frac{7x^2-3x}{9-x^2}\)
c)\(\frac{3}{4x-20}+\frac{15}{50-2x^2}+\frac{7}{6x+30}\)
rút gọn biểu thức
a,\(\frac{x^2-9}{x^3-27}+\frac{1-x^2}{x^3+x^2+x}\)
b\(\frac{x^2-9x}{x^2-8x-9}-\frac{x^2+2}{x^2+x}\)
c,\(\frac{x^3-x^2+x}{x^3+1}-\frac{x^2+x}{x^2+2x+1}\)
d,\(\frac{x^2+x-6}{2x+6}+\frac{x^2-6x+5}{x^2+5x}\)
$\frac{4x+3}{5}$ -$\frac{6x-2}{7}$ =$\frac{5x+4}{3}$ +3
b.
$\frac{x+4}{5}$ -x+4=$\frac{x}{3}$ -$\frac{x-2}{2}$
c.$\frac{5x+2}{6}$ -$\frac{8x-1}{3}$ =$\frac{4x+2}{5}$ -5
d.$\frac{2x+3}{3}$ =$\frac{5-4}{2}$
e. $\frac{5x+3}{12}$ =$\frac{1+2x}{9}$
f.$\frac{7x-1}{6}$ =$\frac{16-x}{5}$
g. $\frac{x-3}{5}$ =6-$\frac{1-2x}{3}$
h. $\frac{3x-2}{6}$ -5=$\frac{3-2(x+7)}{4}$
giúp vs ạ, cần gấp
d: =>4x+6=15x-12
=>4x-15x=-12-6=-18
=>-11x=-18
hay x=18/11
e: =>\(45x+27=12+24x\)
=>21x=-15
hay x=-5/7
f: =>35x-5=96-6x
=>41x=101
hay x=101/41
g: =>3(x-3)=90-5(1-2x)
=>3x-9=90-5+10x
=>3x-9=10x+85
=>-7x=94
hay x=-94/7
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