Giai pt
- \(\frac{x+5}{x^2-5x}-\frac{x-5}{2x^2+10x}=\frac{x+25}{2x^2-50}\)
- \(\dfrac{\left(x+2\right)^2}{2x-3}-1=\dfrac{x^2+10}{2x-3}\)
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Giai pt
- \(\frac{^{\left(x+2\right)^2}}{2x-3}-1=\frac{x^2+10}{2x-3}\)
- \(\frac{x+5}{x^2-5x}-\frac{x-5}{2x^2+10x}=\frac{x+25}{2x^2-50}\)
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) \(\frac{7}{8x}+\frac{5-x}{4x^2-8x}=\frac{x-1}{2x.\left(x-2\right)}+\frac{1}{8x-16}\)
B2 : Giải ptr :
a) \(\left(2x+5\right)^2=\left(x+2\right)^2\)
b) \(3-4x.\left(25-2x\right)=8x^2+x-300\)
c) \(\frac{x+5}{x^2-5x}-\frac{x-5}{2x^2+10x}=\frac{x+25}{2x^2-50}\)
a, (2x+5)mũ 2=(x+2) mũ 2
=.> (2x+5) mũ 2-(x+2) mũ 2=0
=> (2x+5+x+2)x(2x+5-x-2)=0
=>(3x+7)x(x+3)=0
=>3x+7=0 hoặc x+3=0
3x+7=0=>x=-7/3
x+3=0 =>x=-3
vậy x=-7/3 hoặc x=-3
hok tot
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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) \(\frac{x+5}{x^2-5x}-\frac{x-5}{2x^2+10x}=\frac{x+25}{2x^2-50}\)
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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Giai pt : \(\frac{x+4}{2x^2-5x+2}+\frac{x+1}{2x^2-7x+3}=\frac{2x+5}{2x^2-7x+3}\left(1\right)\)
Thực hiện các phép đổi tương đương , ta đưa ( 1 ) về dạng :
\(\frac{x+4}{2x^2-5x+2}-\frac{x+4}{2x^2-7x+3}=0\)
\(\Leftrightarrow\left(x+4\right)\left(\frac{1}{2x^2-5x+2}-\frac{1}{2x^2-7x+3}\right)=0\)
\(\Leftrightarrow\frac{\left(x+4\right)\left(1-2x\right)}{\left(2x^2-5x+2\right)\left(2x^2-7x+3\right)}=0\)
\(\Leftrightarrow\left(x+4\right)\left(1-2x\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=-4\\x=\frac{1}{2}\end{array}\right.\)
Thữ vào mẫu thức : Với \(x=\frac{1}{2}\) thì \(2x^2-5x+2=0\)
Với \(x=-4\) thì \(\left(2x^2-5x+2\right)\left(2x^2-7x+3\right)\ne0\)
Vậy phương trình ( 1 ) là cho nghiệm duy nhất là \(x=-4\)
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a ) \(\frac{x+5}{x^2-5x}\)- \(\frac{x-5}{2x^2+10x}\)= \(\frac{x+25}{2x^2-50}\)
b ) \(\frac{1}{x-1}-\frac{3x^2}{x^3-1}=\frac{2x}{x^2+x+1}\)
c ) \(\frac{7}{8x}+\frac{5-x}{4x^2-8x}-\frac{x-1}{2x\left(x-2\right)}+\frac{1}{8x-16}\)
Giải các pt chứa ẩn ở mẫu sau:
a, \(\frac{12}{8+x^3}=1+\frac{1}{x+2}\)
b,\(\frac{x+25}{2x^2-50}-\frac{x+5}{x^2-5x}=\frac{5-x}{2x^2+10x}\)
c,\(\frac{4}{x^2+2x-3}=\frac{2x-5}{x+3}-\frac{2x}{x-1}\)
Giải các phương trình sau:
a) \(\frac{x+5}{x^2-5x}-\frac{x+25}{2x^2-50}=\frac{x-5}{2x^2+10x}\).
b) \(\frac{1}{3-x}-\frac{1}{x+1}=\frac{x}{x-3}-\frac{\left(x-1\right)^2}{x^2-2x-3}\).
c) \(\frac{x+1}{x^2+x+1}-\frac{x-1}{x^2-x+1}=\frac{2\left(x+2\right)^2}{x^6-1}\).
d) \(\frac{x}{x-3}-\frac{x}{x-5}=\frac{x}{x-4}-\frac{x}{x-6}\).