Tìm GTLN của
\(B=\frac{5x^2-10x+42}{x^2+2x+7}\)
\(C=\frac{2x}{x^2+2x+1}\)
Những câu hỏi liên quan
Rút gọn
a)\(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\)
b)\(\left\{\frac{2x+1}{2x-1}-\frac{2x-1}{2x+1}\right\}:\frac{4x}{10x-5}\)
c)\(\frac{x^2+x}{5x^2-10x+5}:\frac{3x+3}{5x-5}\)
\(a,\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\) (x khác -3; khác 0)
\(=\frac{3}{2\left(x+3\right)}-\frac{x-6}{2x.\left(x+3\right)}=\frac{3x}{2x.\left(x+3\right)}-\frac{x-6}{2x.\left(x+3\right)}=\frac{3x-x+6}{2x.\left(x+3\right)}=\frac{2x+6}{x.\left(2x+6\right)}=\frac{1}{x}\)
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\(b,\left(\frac{2x+1}{2x-1}-\frac{2x-1}{2x+1}\right):\frac{4x}{10x-5}\) (x khác 0 , khác 1/2 khác -1/2 )
\(=\left(\frac{\left(2x+1\right)^2}{\left(2x-1\right)\left(2x+1\right)}-\frac{\left(2x-1\right)^2}{\left(2x-1\right)\left(2x+1\right)}\right).\frac{10x-5}{4x}\)
\(=\left(\frac{4x^2+4x+1}{\left(2x-1\right)\left(2x+1\right)}-\frac{4x^2-4x+1}{\left(2x-1\right)\left(2x+1\right)}\right).\frac{10x-5}{4x}\)
\(=\frac{8x}{\left(2x-1\right)\left(2x+1\right)}.\frac{5.\left(2x-1\right)}{4x}=\frac{10}{2x+1}\)
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\(c,\frac{x^2+x}{5x^2-10x+5}:\frac{3x+3}{5x-5}\) (x khác 1 ; khác -1)
\(=\frac{x.\left(x+1\right)}{5.\left(x^2-2x+1\right)}.\frac{5x-5}{3x+3}=\frac{x.\left(x+1\right)}{5.\left(x-1\right)^2}.\frac{5\left(x-1\right)}{3.\left(x+1\right)}=\frac{x}{3.\left(x-1\right)}=\frac{x}{3x-3}\)
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Rút gọna) frac{3}{2x+6}-frac{x-6}{2x^2+6x}b) (frac{2x+1}{2x-1}-frac{2x-1}{2x+1}) / frac{4x}{10x-5}c) frac{x^2 +x}{5x^2-10x+5}/ frac{3x+3}{5x-5}Cho biểu thức Afrac{x^2+2x}{2x+10}+frac{x-5}{x}-frac{50-5x}{2xleft(x+5right)}a) Tìm điệu kiện xác địnhb) Rút gọn Ac) Tìm x để A1
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Rút gọn
a) \(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\)
b) (\(\frac{2x+1}{2x-1}-\frac{2x-1}{2x+1}\)) / \(\frac{4x}{10x-5}\)
c) \(\frac{x^2 +x}{5x^2-10x+5}\)/ \(\frac{3x+3}{5x-5}\)
Cho biểu thức
A=\(\frac{x^2+2x}{2x+10}\)+\(\frac{x-5}{x}\)-\(\frac{50-5x}{2x\left(x+5\right)}\)
a) Tìm điệu kiện xác định
b) Rút gọn A
c) Tìm x để A=1
Rút gọn
a)\(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\)
b)\(\left\{\hept{\begin{cases}2x+1\\2x-1\end{cases}-\frac{2x-1}{2x+1}}\right\}:\frac{4x}{10x-5}\)
c)\(\frac{x^2+x}{5x^2-10x+5}:\frac{3x+3}{5x-5}\)
Thực hiện phép tính
a) \(\left(\frac{2x+1}{2x-2}+\frac{3}{x^2-1}-\frac{x+3}{2x+2}\right).\frac{4x^2-4}{3}\)
b) \(\left(\frac{5x+2}{x^2-10x}+\frac{5x-2}{x^2+10x}\right).\frac{x^2-100}{x^2+4}\)
c) \(\frac{1}{x-1}-\frac{x^3-x}{x^2+1}.\left(\frac{1}{x^2-2x+1}+\frac{1}{1-x^2}\right)\)
Cho \(A=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{50-5x}{2x^2+10x}\)
a) Tìm diều kiện của x
b) tìm x để A=1
HELPPPPPPPPPPPPPPPP!
A, Để biểu thức A có nghĩa thì
\(2x+10\ne0\Rightarrow x\ne-5\)
\(x\ne0\)
\(2x^2+10x\ne0\Rightarrow x\ne0;x\ne-5\)
Vậy điều kiện của x là \(x\ne0;x\ne-5\)
b) Ta có:
\(A=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{50-5x}{2x^2+10x}\)
\(A=\frac{x\cdot\left(x^2+2x\right)+\left(x-5\right)\cdot\left(2x+10\right)+50-5x}{2x^2+10x}\)
\(A=\frac{x^3+4x^2-5x}{2x^2+10x}\)
\(A=\frac{x\cdot\left(x-1\right)\cdot\left(x+5\right)}{2x\cdot\left(x+5\right)}\)
\(A=\frac{x-1}{2}\)
Để A=1 thì ta có\(\frac{x-2}{2}=1\Leftrightarrow x-2=2\Leftrightarrow x=4\)
Vậy x=4 thì A=1
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Giải phương trìnha) frac{4}{20-6x-2x^2}+ frac{x^2+4x}{x^2+5x}-frac{x+3}{2-x}+30b)frac{x+5}{x^2-5x}-frac{x-5}{2x^2-10x}+10frac{x+25}{2x^2-50}c) frac{7}{8x}+frac{5-x}{4x^2-8x}frac{x-1}{2x.left(x-2right)}+frac{1}{8x-16}c) frac{7}{8x}+frac{5-x}{4x^2-8x}frac{x-1}{2x.left(x-2right)}+frac{1}{8x-16}
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Giải phương trình
a) \(\frac{4}{20-6x-2x^2}\)+ \(\frac{x^2+4x}{x^2+5x}-\frac{x+3}{2-x}+3=0\)
b)\(\frac{x+5}{x^2-5x}-\frac{x-5}{2x^2-10x}+10=\frac{x+25}{2x^2-50}\)
c) \(\frac{7}{8x}+\frac{5-x}{4x^2-8x}=\frac{x-1}{2x.\left(x-2\right)}+\frac{1}{8x-16}\)
c) \(\frac{7}{8x}+\frac{5-x}{4x^2-8x}=\frac{x-1}{2x.\left(x-2\right)}+\frac{1}{8x-16}\)
A=4x^2=4xy+17y^2-8y+1
B=\(\frac{x^2-2}{x^2+2}\)
C=\(\frac{5x^2-10+3}{\left(x-1\right)^2}\)
D=\(\frac{3x^2-8x+6}{x^2-2x+1}\)
Tìm GTLN của biểu thức sau
C=\(\frac{x^2+5x+7}{x^2+4x+4}\)
D=\(\frac{x^2-2x+2020}{x^2}\)
c) \(\frac{x+5}{x^2-5x}-\frac{x-5}{2x^2+10x}=\frac{x+25}{2x^2-50}\)
d) \(\frac{7}{8x}+\frac{5-x}{4x^2-8x}=\frac{x-1}{2x\left(x-2\right)}+\frac{1}{8x-16}\)
e) \(\frac{1}{x-1}-\frac{3x^2}{x^3-1}=\frac{2x}{x^2+x+1}\)
ĐK: ...
c) \(\frac{x+5}{x^2-5x}-\frac{x-5}{2x^2+10x}=\frac{x+25}{2x^2-50}\)
\(\Leftrightarrow\frac{2\left(x+5\right)^2}{2x\left(x-5\right)\left(x+5\right)}-\frac{\left(x-5\right)^2}{2x\left(x+5\right)\left(x-5\right)}=\frac{x\left(x+25\right)}{2x\left(x-5\right)\left(x+5\right)}\)
\(\Leftrightarrow2x^2+20x+50-x^2+10x-25=x^2+25x\)
\(\Leftrightarrow5x+25=0\)
\(\Leftrightarrow x=-5\)( ko t/m )
d) tương tự, ngại tính lắm
e) \(\frac{1}{x-1}-\frac{3x^2}{x^3-1}=\frac{2x}{x^2+x+1}\)
\(\Leftrightarrow\frac{x^2+x+1}{x^3-1}-\frac{3x^2}{x^3-1}=\frac{2x\left(x-1\right)}{x^3-1}\)
\(\Leftrightarrow4x^2-3x-1=0\)
\(\Leftrightarrow\left(x-1\right)\left(4x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\left(l\right)\\x=\frac{-1}{4}\left(c\right)\end{matrix}\right.\)
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Giải phương trình
a) \(\frac{4}{20-6x-2x^2}\)+ \(\frac{x^2+4x}{x^2+5x}-\frac{x+3}{2-x}+3=0\)
b)\(\frac{x+5}{x^2-5x}-\frac{x-5}{2x^2-10x}+10=\frac{x+25}{2x^2-50}\)
c) \(\frac{7}{8x}+\frac{5-x}{4x^2-8x}=\frac{x-1}{2x.\left(x-2\right)}+\frac{1}{8x-16}\)
