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1: Ta có: \(\dfrac{5x^2-12}{x^2-1}+\dfrac{3}{x-1}=\dfrac{5x}{x+1}\)
\(\Leftrightarrow\dfrac{5x^2-12}{\left(x-1\right)\left(x+1\right)}+\dfrac{3x+3}{\left(x-1\right)\left(x+1\right)}=\dfrac{5x^2-5x}{\left(x+1\right)\left(x-1\right)}\)
Suy ra: \(5x^2+3x-9=5x^2-5x\)
\(\Leftrightarrow8x=9\)
hay \(x=\dfrac{9}{8}\left(tm\right)\)
2: Ta có: \(\dfrac{3}{x-5}-\dfrac{15-3x}{x^2-25}=\dfrac{3}{x+5}\)
\(\Leftrightarrow\dfrac{3x+15}{\left(x-5\right)\left(x+5\right)}+\dfrac{3x-15}{\left(x-5\right)\left(x+5\right)}=\dfrac{3x-15}{\left(x+5\right)\left(x-5\right)}\)
Suy ra: \(6x=3x-15\)
\(\Leftrightarrow3x=-15\)
hay \(x=-5\left(loại\right)\)
2. ĐKXĐ: $x\neq \pm 5$
PT \(\Leftrightarrow \frac{3}{x-5}+\frac{3x-15}{x^2-25}=\frac{3}{x+5}\)
\(\Leftrightarrow \frac{3}{x-5}+\frac{3(x-5)}{(x-5)(x+5)}=\frac{3}{x+5}\)
\(\Leftrightarrow \frac{3}{x-5}+\frac{3}{x+5}=\frac{3}{x+5}\Leftrightarrow \frac{3}{x-5}=0\) (vô lý)
Vậy pt vô nghiệm.
a: 3x-5>15-x
=>4x>20
hay x>5
b: \(3\left(x-2\right)\left(x+2\right)< 3x^2+x\)
=>3x2+x>3x2-12
=>x>-12
1) -2(x - 3) + 5x (x - 1) = 5x (x + 1)
<=> -2x + 6 + 5x2 - 5x = 5x2 + 5x
<=> 6 = 5x2 + 5x + 2x - 5x2 + 5x
<=> 6 = 12x
<=> \(\dfrac{6}{12}\) = x = 0,5
vậy tập nghiệm S ={0,5}
2) 7 - (2x + 4) = -(x + 4)
<=> 7 - 2x - 4 = -x - 4
<=> 7 - 4 + 4 = -x + 2x
<=> 7 = x
vậy tập nghiệm S ={7}
\(a,2x-5=-x+4\\ \Leftrightarrow3x=9\\ \Leftrightarrow x=3\\ b,\left(4x-10\right)\left(25+5x\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}4x-10=0\\25+5x=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-5\end{matrix}\right.\\ c,\dfrac{x}{3}-\dfrac{2x+1}{2}=\dfrac{x}{6}-x\\ \Leftrightarrow\dfrac{2x}{6}-\dfrac{3\left(2x+1\right)}{6}-\dfrac{x}{6}+\dfrac{6x}{6}=0\\ \Leftrightarrow2x-6x-3-x+6x=0\\ \Leftrightarrow x-3=0\\ \Leftrightarrow x=3\)
d, ĐKXĐ:\(x\ne-2,x\ne3\)
\(1+\dfrac{x}{3-x}=\dfrac{5x}{\left(x+2\right)\left(3-x\right)}+\dfrac{2}{x+2}\\ \Leftrightarrow\dfrac{\left(x+2\right)\left(3-x\right)}{\left(x+2\right)\left(3-x\right)}+\dfrac{x\left(x+2\right)}{\left(x+2\right)\left(3-x\right)}-\dfrac{5x}{\left(x+2\right)\left(3-x\right)}-\dfrac{2\left(3-x\right)}{\left(x+2\right)\left(3-x\right)}=0\\ \Leftrightarrow\dfrac{-x^2+x+6}{\left(x+2\right)\left(3-x\right)}+\dfrac{x^2+2x}{\left(x+2\right)\left(3-x\right)}-\dfrac{5x}{\left(x+2\right)\left(3-x\right)}-\dfrac{6-2x}{\left(x+2\right)\left(3-x\right)}=0\)
\(\Leftrightarrow\dfrac{-x^2+x+6+x^2+2x-5x-6+2x}{\left(x+2\right)\left(3-x\right)}=0\\ \Rightarrow0=0\left(luôn.đúng\right)\)
Ta có: 5x + 3x2 = 0
<=> x(3x + 5) = 0
<=> \(\orbr{\begin{cases}x=0\\3x+5=0\end{cases}}\)
<=> \(\orbr{\begin{cases}x=0\\x=-\frac{5}{3}\end{cases}}\) Vậy S = {0; -5/3)
5(x2 - 2x) = (3 + 5x)(x - 1)
<=> 5x2 - 10x = 5x2 - 2x - 3
<=> 5x2 - 10x - 5x2 + 2x = -3
<=> -8x = -3
<=> x = 3/8 Vậy S = {3/8}
(4x + 3)2 = 4(x - 1)2
<=> (4x + 3)2 - (2x - 2)2 = 0
<=> (4x + 3 - 2x + 2)(4x +3 + 2x - 2) = 0
<=> (2x + 5)(6x + 1) = 0
<=> \(\orbr{\begin{cases}2x+5=0\\6x+1=0\end{cases}}\)
<=> \(\orbr{\begin{cases}x=-\frac{5}{2}\\x=-\frac{1}{6}\end{cases}}\) Vậy S = {-5/3; -1/6}
a) 5x + 3.x2 = 0
<=>x . ( 5 + 3x ) = 0
<=> \(\orbr{\begin{cases}x=0\\5+3.x=0\end{cases}}\)
<=>\(\orbr{\begin{cases}x=0\\z=-\frac{5}{3}\end{cases}}\)
Nghiệm cuối cùng là :{ 0;\(-\frac{5}{3}\)}
b) 5.( x2 - 2.x ) = ( 3 + 5.x ) . ( x- 1 )
<=>5.x2 - 10.x = 3.x -3 + 5.x2 - 5.x
<=> -10.x = 3.x - 3-5.x
<=> -10.x = -2.x - 3
<=> -8.x = -3
<=> x = \(\frac{3}{8}\)
Vậy x = \(\frac{3}{8}\)
c) ( 4x + 3 )2 = 4. ( x - 1 )2
<=> 16.x2 + 24.x + 9 = 4.( x2 -2.x + 1 )
<=> 16.x2+24.x + 9 = 4.x2 -8.x + 4
<=> 16.x2 +24.x + 9 -4.x2 + 8.x - 4= 0
<=> 12.x2 + 32.x + 5 = 0
<=> 12.x2 + 30.x + 2.x + 5 = 0
<=> 6.x . ( 2.x + 5 ) + 2.x + 5 =0
<=> ( 2.x + 5 ) . ( 6.x + 1 ) =0
<=> \(\orbr{\begin{cases}2.x+5=0\\6.x+1=0\end{cases}}\)
<=> \(\orbr{\begin{cases}x=-\frac{5}{2}\\x=-\frac{1}{6}\end{cases}}\)
Nghiệm cuối cùng là : { \(-\frac{5}{2};-\frac{1}{6}\)}
`|5x| = - 3x + 2`
Nếu `5x>=0<=> x>=0` thì phương trình trên trở thành :
`5x =-3x+2`
`<=> 5x +3x=2`
`<=> 8x=2`
`<=> x= 2/8=1/4` ( thỏa mãn )
Nếu `5x<0<=>x<0` thì phương trình trên trở thành :
`-5x = -3x+2`
`<=>-5x+3x=2`
`<=> 2x=2`
`<=>x=1` ( không thỏa mãn )
Vậy pt đã cho có nghiệm `x=1/4`
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`6x-2<5x+3`
`<=> 6x-5x<3+2`
`<=>x<5`
Vậy bpt đã cho có tập nghiệm `x<5`