Tìm x:
\(\dfrac{3x-1}{40-5x}=\dfrac{25-3x}{5x-34}\)
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13 tháng 6 2016
Ta có :
\(\frac{3x-1}{40-5x}=\frac{25-3x}{5x-34}\)
\(=>\left(3x-1\right)\left(5x-34\right)=\left(40-5x\right)\left(25-3x\right)\)
\(=>15x^2-102x-5x+34=1000-120x-125x+15x^2\)
\(=>15x^2-107x+34=1000-245x+15x^2\)
\(=>34-107x=1000-245x\)
\(=>1000-245x+107x=34\)
\(=>1000-138x=34\)
\(=>138x=1000-34=966\)
\(=>x=\frac{966}{138}=7\)
4 tháng 11 2017
=>(2x+3).(10x+2)=(5x+2).(4x+5)
=>(2x.10x)+(2x.2)+(3.10x)+(3.2)=(5x.4x)+(5x.5)+(2.4x)+(2.5)
=>20x2+4x+30x+6=20x2+25x+8x+10
=>20x2-20x2+4x-8x+30x-25x=10-6
=>0+4x-8x+30x-25x=4
=>-4x+30x-25x=4
=>26x-25x=4
=>x=4
B)=>(3x-1).(5x-34)=(40-5x).(25-3x)
=>15x2-102x-5x+34=1000-120x-125x+15x2
=>15x2-107x+34=1000-245x+15x2
=>15x2-15x2-107x+245x=1000-34
=>0-107x+245x=966
=>138x=966
=>x=7
12 tháng 8 2018
A,=>(2x+3).(10x+2)=(5x+2).(4x+5)
=>(2x.10x)+(2x.2)+(3.10x)+(3.2)=(5x.4x)+(5x.5)+(2.4x)+(2.5)
=>20x2+4x+30x+6=20x2+25x+8x+10
=>20x2-20x2+4x-8x+30x-25x=10-6
=>0+4x-8x+30x-25x=4
=>-4x+30x-25x=4
=>26x-25x=4
=>x=4
8 tháng 12 2021
\(a,=\dfrac{15x+25-25x+x^2}{5x\left(x-5\right)}=\dfrac{\left(x-5\right)^2}{5x\left(x-5\right)}=\dfrac{x-5}{5x}\\ b,=\dfrac{x^2-x-2+x-7+x+3}{\left(x+3\right)\left(x-2\right)}=\dfrac{x^2+x-6}{x^2+x-6}=1\)
8 tháng 12 2021
\(a,\dfrac{3x+5}{x^2-5x}+\dfrac{25-x}{25-5x}\)
\(=\dfrac{3x+5}{x\left(x-5\right)}+\dfrac{25-x}{5\left(5-x\right)}\)
\(=\dfrac{-3x-5}{x\left(5-x\right)}+\dfrac{25-x}{5\left(5-x\right)}\)
\(=\dfrac{5\left(-3x-5\right)}{5x\left(5-x\right)}+\dfrac{x\left(25-x\right)}{5x\left(5-x\right)}\)
\(=\dfrac{-15x-25+25x-x^2}{5x\left(5-x\right)}\)
\(=\dfrac{10x-25-x^2}{5x\left(5-x\right)}\)
\(=\dfrac{-\left(5-x\right)^2}{5x\left(5-x\right)}\)
\(=\dfrac{-5+x}{5x}\)
\(b,\dfrac{x+1}{x+3}+\dfrac{x-7}{x^2+x-6}+\dfrac{1}{x-2}\)
\(=\dfrac{x+1}{x+3}+\dfrac{x-7}{\left(x+3\right)\left(x-2\right)}+\dfrac{1}{x-2}\)
\(=\dfrac{\left(x+1\right)\left(x-2\right)}{\left(x+3\right)\left(x-2\right)}+\dfrac{x-7}{\left(x+3\right)\left(x-2\right)}+\dfrac{x+3}{\left(x+3\right)\left(x-2\right)}\)
\(=\dfrac{x^2-2x+x-2+x-7+x+3}{\left(x+3\right)\left(x-2\right)}\)
\(=\dfrac{x^2+x-6}{\left(x+3\right)\left(x-2\right)}\)
\(=\dfrac{x^2+x-6}{x^2-2x+3x-6}\)
\(=\dfrac{x^2+x-6}{x^2+x-6}\)
\(=1\)
TT
1
16 tháng 10 2015
\(\frac{3x-1}{40-5x}=\frac{25-3x}{5x-34}\)
=> (3x-1).(5x-34)=(40-5x).(25-3x)
=> 3x.(5x-34)-(5x-34)= 40.(25-3x)-5x.(25-3x)
=> 15x2-102x-5x+34= 1000-120x-125x+15x2
=> 15x2- 107x+34 = 1000-245x+15x2
=> 107x+34 =1000-245x
=> 138x=966
=> x=7
26 tháng 10 2018
\(\frac{3x-1}{40-5x}=\frac{25-3x}{5x-34}\)
\(\Rightarrow\left(3x-1\right)\left(5x-34\right)=\left(40-5x\right)\left(25-3x\right)\)
\(\Rightarrow3x\left(5x-34\right)-1\left(5x-34\right)=40\left(25-3x\right)-5x\left(25-3x\right)\)
\(\Rightarrow15x^2-102x-5x+34=1000-120x-125x+15x^2\)
\(\Rightarrow15x^2-107x+34=1000-245x+15x^2\)
\(\Rightarrow-107x+34=1000-245x\)
\(\Rightarrow-107x+245x=1000-34\)
\(\Rightarrow138x=966\)
\(\Rightarrow x=7\)
Mình chắc chắn đáp án này đúng.
19 tháng 8 2021
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 \(x=-5\left(loại\right)\)
AH
Akai Haruma
Giáo viên
19 tháng 8 2021
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.
\(\dfrac{3x-1}{40-5x}=\dfrac{25-3x}{5x-34}\\ \Leftrightarrow\left(3x-1\right)\left(5x-34\right)=\left(25-3x\right)\left(40-5x\right)\\ \Leftrightarrow15x^2-102x-5x+34=1000-125x-120x+15x^2\\ \Leftrightarrow15x^2-15x^2-102x-5x+125x+120x=1000-34\\ \Leftrightarrow138x=966\\ \Leftrightarrow x=\dfrac{966}{138}\\ \Leftrightarrow x=7\)