giải phương trình:
a)\(\left[\frac{a+1}{ãx+1}+\frac{x+1}{x+\frac{1}{a}}-1\right]:\left[\frac{a+1}{\left(x+\frac{1}{a}\right)a}-\frac{a\left(x+1\right)}{ãx+1}+1\right]\)\(=\frac{x}{2}\)
b)\(\frac{x+a}{x-3}+\frac{x+3}{x-a}=2\)
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giải phương trinh:
a)\(\frac{1}{a+b-x}=\frac{1}{a}+\frac{1}{b}-\frac{1}{x}\)
b)\(\frac{1}{\left(x+a\right)^2-1}+\frac{1}{\left(x+1\right)^2-a^2}=\frac{1}{x^2-\left(a+1\right)^2}+\frac{1}{x^2-\left(a-1\right)^2}\)
a)\(\frac{1}{a+b-x}\)=\(\frac{1}{a}\)+\(\frac{1}{b}\)-\(\frac{1}{x}\)\(\Leftrightarrow\)\(\frac{1}{a+b-x}\)+\(\frac{1}{x}\)=\(\frac{a+b}{ab}\)\(\Leftrightarrow\)\(\frac{x+a+b-x}{x\left(a+b-x\right)}\)=\(\frac{a+b}{ab}\)
\(\Leftrightarrow\)\(\frac{a+b}{xa+xb-x^2}\)=\(\frac{a+b}{ab}\)\(\Leftrightarrow\)\(xa+xb-x^2\)=\(ab\)\(\Leftrightarrow\)\(xa+xb-x^2-ab\)=\(0\)
\(\Leftrightarrow\)\(a\left(x-b\right)-x\left(x-b\right)=0\)\(\Leftrightarrow\)\(\left(x-b\right)\left(a-x\right)=0\)\(\Leftrightarrow\)\(x=b;x=a\)
b) \(\Leftrightarrow\)\(\frac{1}{\left(x+a-1\right)\left(x+a+1\right)}+\frac{1}{\left(x+a+1\right)\left(x-a+1\right)}\)=\(\frac{1}{\left(x-a-1\right)\left(x+a+1\right)}+\frac{1}{\left(x-a+1\right)\left(x+a-1\right)}\)\(\Leftrightarrow\)\(\frac{1}{\left(x+a-1\right)\left(x+a+1\right)}-\frac{1}{\left(x-a-1\right)\left(x+a+1\right)}\)=\(\frac{1}{\left(x-a+1\right)\left(x+a-1\right)}-\frac{1}{\left(x+a+1\right)\left(x-a+1\right)}\)\(\Leftrightarrow\)\(\frac{1}{\left(x+a+1\right)}\left(\frac{1}{x+a-1}-\frac{1}{x-a-1}\right)\)=\(\frac{1}{x-a+1}\left(\frac{1}{x+a-1}-\frac{1}{x+a+1}\right)\)\(\Leftrightarrow\)\(\frac{1}{x+a+1}.\frac{-2a}{\left(x+a-1\right)\left(x-a-1\right)}=\frac{1}{x-a+1}.\frac{2}{\left(x+a-1\right)\left(x+a+1\right)}\)(Quy dong phan so ttrong dau ngoac)
\(\Leftrightarrow\)\(\frac{-2a}{x-a-1}=\frac{2}{x-a+1}\)\(\Leftrightarrow\)\(-2a\left(x-a+1\right)=2\left(x-a-1\right)\)\(\Leftrightarrow\)\(-ax+a^2-a=x-a-1\)\(\Leftrightarrow\)\(-ax-x+a^2-1=0\)\(\Leftrightarrow\)\(\left(a+1\right)\left(-x+a-1\right)=0\)
neu a+1=0 thi phuong trinh co vo so nghiem, neu a+1\(\ne\)0 thi x=a-1
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Giải phương trình :
\(a,\frac{1}{a+b-x}=\frac{1}{a}+\frac{1}{b}-\frac{1}{x}\)(x là ẩn số )
\(b,\frac{\left(b-c\right)\left(1+a\right)^2}{x+a^2}+\frac{\left(c-a\right)\left(1+b\right)^2}{x+b^2}+\frac{\left(a-b\right)\left(1+c\right)^2}{x+c^2}\)
Cho :\(A=\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{1}{x+3};B=\frac{a}{x\left(x+a\right)}+\frac{a}{\left(x+a\right)\left(x+2a\right)}+\frac{a}{\left(x+2a\right)\left(x+3a\right)}+\frac{1}{x+3a}\)CMR : A = B
Giải phương trình :
a, \(\frac{1}{a+b-x}=\frac{1}{a}+\frac{1}{b}+\frac{1}{x}\)
b, \(\frac{\left(b-c\right)\left(1+a\right)^2}{x+a^2}+\frac{\left(c-a\right)\left(1+b\right)^2}{x+b^2}+\frac{\left(a+b\right)\left(1+c\right)^2}{x+c^2}\)
Giải phương trình
\(\frac{1}{\left(x+a\right)^2-1}+\frac{1}{\left(x+1\right)^2-a^2}=\frac{1}{x^2-\left(a+1\right)^2}+\frac{1}{x^2-\left(a-1\right)^2}\)
Giải phương trình:
a,\(\frac{1}{a+b-x}=\frac{1}{a}+\frac{1}{b}+\frac{1}{x}\)(x là ẩn số)
b,\(\frac{\left(b-c\right)\left(1+a\right)^2}{x+a^2}+\frac{\left(c-a\right)\left(1+c\right)^2}{x+b^2}+\frac{\left(a-b\right)\left(1+c\right)^2}{x+c^2}=0\)
Giúp hộ!!!
giải phương trình : \(\frac{1}{\left(x+a\right)^2-1}+\frac{1}{\left(x+1\right)^2-a^2}=\frac{1}{x^2-\left(a+1\right)^2}+\frac{1}{x^2-\left(a-1\right)^2}\)( a là hằng số)
Bài 1: Cho a,b,c đôi một khác nhau. CMR:frac{left(x-bright)left(x-cright)}{left(a-bright)left(a-cright)}+frac{left(x-cright)left(x-aright)}{left(b-cright)left(b-aright)}+frac{left(x-aright)left(x-bright)}{left(c-aright)left(c-bright)}11Bài 2: CMR: nếu frac{1}{x}-frac{1}{y}-frac{1}{z}1và xy+z thì:frac{1}{x^2}+frac{1}{y^2}+frac{1}{z^2}1
Đọc tiếp
Bài 1: Cho a,b,c đôi một khác nhau. CMR:
\(\frac{\left(x-b\right)\left(x-c\right)}{\left(a-b\right)\left(a-c\right)}+\frac{\left(x-c\right)\left(x-a\right)}{\left(b-c\right)\left(b-a\right)}+\frac{\left(x-a\right)\left(x-b\right)}{\left(c-a\right)\left(c-b\right)}=1\)=1
Bài 2: CMR: nếu \(\frac{1}{x}-\frac{1}{y}-\frac{1}{z}=1\)và x=y+z thì:
\(\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=1\)
Giải phương trình:
a,\(\frac{5-x}{4x^2-8x}+\frac{7}{8x}=\frac{x-1}{2x\left(x-2\right)}+\frac{1}{8x-16}\)
b,\(\frac{x-49}{50}+\frac{x-50}{49}=\frac{49}{x-50}+\frac{50}{x-49}\)
c,\(\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}=\frac{1}{x+3}\)