giải phương trình:
\(\dfrac{2}{x-3}\) + \(\dfrac{3}{x+3}\)=\(\dfrac{7x+5}{x^2-9}\)
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F
1
H
28 tháng 11 2023
\(\dfrac{x^2-x}{x+3}-\dfrac{x^2}{x-3}=\dfrac{7x^2-3x}{9-x^2}\\ \Leftrightarrow\dfrac{x^2-x}{x+3}-\dfrac{x^2}{x-3}=-\dfrac{7x^2-3x}{\left(x-3\right)\left(x+3\right)}\\ đkxđ:\left\{{}\begin{matrix}x-3\ne0\\x+3\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne3\\x\ne-3\end{matrix}\right.\\ \Leftrightarrow\dfrac{\left(x^2-x\right)\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}-\dfrac{x^2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\dfrac{7x^2-3x}{\left(x-3\right)\left(x+3\right)}=0\\ \Leftrightarrow\dfrac{x^3-3x^2-x^2+3x-x^3-3x^2+7x^2-3x}{\left(x-3\right)\left(x+3\right)}=0\\ \Leftrightarrow\dfrac{0}{\left(x-3\right)\left(x+3\right)}=0\\ \Rightarrow0=0\left(luon.dung\right)\)
Y
1
TA
28 tháng 5 2021
ĐK: ` x \ne \pm 3`
`(x^2-x)/(x+3)-(x^2)/(x-3)=(7x^2-3x)/(9-x^2)`
`<=> (x^2-x)(x-3)-x^2 (x+3) = -(7x^2-3x)`
`<=> −7x^2+3x=-7x^2+3x`
`<=> 0x=0 forall x`
Vậy `S=RR \\ {+-3}`.
19 tháng 2 2022
a: \(\Leftrightarrow7\left(7-3x\right)+12\left(5x+2\right)=84\left(x+13\right)\)
\(\Leftrightarrow49-21x+60x+24=84x+1092\)
\(\Leftrightarrow39x-84x=1092-73\)
=>-45x=1019
hay x=-1019/45
b: \(\Leftrightarrow21\left(x+3\right)-14=4\left(5x+9\right)-7\left(7x-9\right)\)
=>21x+63-14=20x+36-49x+63
=>21x+49=-29x+99
=>50x=50
hay x=1
c: \(\Leftrightarrow7\left(2x+1\right)-3\left(5x+2\right)=21x+63\)
=>14x+7-15x-6-21x-63=0
=>-22x-64=0
hay x=-32/11
d: \(\Leftrightarrow35\left(2x-3\right)-15\left(2x+3\right)=21\left(4x+3\right)-17\cdot105\)
=>70x-105-30x-45=84x+63-1785
=>40x-150-84x+1722=0
=>-44x+1572=0
hay x=393/11
3 tháng 2 2022
a: =>10x-4=15-9x
=>19x=19
hay x=1
b: \(\Leftrightarrow3\left(10x+3\right)=36+4\left(8x+6\right)\)
=>30x+9=36+32x+24
=>30x-32x=60-9
=>-2x=51
hay x=-51/2
c: \(\Leftrightarrow2x+\dfrac{6}{5}=5-\dfrac{13}{5}-x\)
=>3x=6/5
hay x=2/5
d: \(\Leftrightarrow\dfrac{7x}{8}-\dfrac{5\left(x-9\right)}{1}=\dfrac{20x+1.5}{6}\)
\(\Leftrightarrow21x-120\left(x-9\right)=4\left(20x+1.5\right)\)
=>21x-120x+1080=80x+60
=>-179x=-1020
hay x=1020/179
e: \(\Leftrightarrow5\left(7x-1\right)+60x=6\left(16-x\right)\)
=>35x-5+60x=96-6x
=>95x+6x=96+5
=>x=1
f: \(\Leftrightarrow6\left(x+4\right)+30\left(-x+4\right)=10x-15\left(x-2\right)\)
=>6x+24-30x+120=10x-15x+30
=>-24x+96=-5x+30
=>-19x=-66
hay x=66/19
7 tháng 3 2021
a) ĐKXĐ: \(x\ne1\)
Ta có: \(\dfrac{7x-3}{x-1}=\dfrac{2}{3}\)
\(\Leftrightarrow3\left(7x-3\right)=2\left(x-1\right)\)
\(\Leftrightarrow21x-9=2x-2\)
\(\Leftrightarrow21x-2x=-2+9\)
\(\Leftrightarrow19x=7\)
\(\Leftrightarrow x=\dfrac{7}{19}\)
Vậy: \(S=\left\{\dfrac{7}{19}\right\}\)
5 tháng 1
a: ĐKXĐ: \(x\notin\left\{2;5\right\}\)
\(\dfrac{6x+1}{x^2-7x+10}+\dfrac{5}{x-2}=\dfrac{3}{x-5}\)
=>\(\dfrac{6x+1}{\left(x-2\right)\left(x-5\right)}+\dfrac{5}{x-2}=\dfrac{3}{x-5}\)
=>\(6x+1+5\left(x-5\right)=3\left(x-2\right)\)
=>6x+1+5x-25-3x+6=0
=>8x-18=0
=>8x=18
=>\(x=\dfrac{9}{4}\left(nhận\right)\)
b: Đề thiếu vế phải rồi bạn
c: ĐKXĐ: \(x\notin\left\{-1;3\right\}\)
\(\dfrac{1}{3-x}-\dfrac{1}{x+1}=\dfrac{x}{x-3}-\dfrac{\left(x-1\right)^2}{x^2-2x-3}\)
\(\Leftrightarrow\dfrac{-1}{x-3}-\dfrac{1}{x+1}-\dfrac{x}{x-3}=\dfrac{-\left(x-1\right)^2}{\left(x-3\right)\left(x+1\right)}\)
=>\(\dfrac{x+1}{x-3}+\dfrac{1}{x+1}=\dfrac{\left(x-1\right)^2}{\left(x-3\right)\left(x+1\right)}\)
=>\(\left(x+1\right)^2+x-3=\left(x-1\right)^2\)
=>\(x^2+2x+1+x-3=x^2-2x+1\)
=>\(3x-2=-2x+1\)
=>5x=3
=>\(x=\dfrac{3}{5}\left(nhận\right)\)
9 tháng 2 2021
b)
ĐKXĐ: \(x\notin\left\{2;3;\dfrac{1}{2}\right\}\)
Ta có: \(\dfrac{x+4}{2x^2-5x+2}+\dfrac{x+1}{2x^2-7x+3}=\dfrac{2x+5}{2x^2-7x+3}\)
\(\Leftrightarrow\dfrac{x+4}{\left(x-2\right)\left(2x-1\right)}+\dfrac{x+1}{\left(x-3\right)\left(2x-1\right)}=\dfrac{2x+5}{\left(2x-1\right)\left(x-3\right)}\)
\(\Leftrightarrow\dfrac{\left(x+4\right)\left(x-3\right)}{\left(x-2\right)\left(2x-1\right)\left(x-3\right)}+\dfrac{\left(x+1\right)\left(x-2\right)}{\left(x-2\right)\left(x-3\right)\left(2x-1\right)}=\dfrac{\left(2x+5\right)\left(x-2\right)}{\left(2x-1\right)\left(x-3\right)\left(x-2\right)}\)
Suy ra: \(x^2-3x+4x-12+x^2-2x+x-2=2x^2-4x+5x-10\)
\(\Leftrightarrow2x^2-14=2x^2+x-10\)
\(\Leftrightarrow2x^2-14-2x^2-x+10=0\)
\(\Leftrightarrow-x-4=0\)
\(\Leftrightarrow-x=4\)
hay x=-4(nhận)
Vậy: S={-4}
26 tháng 1
a: \(x-3\left(2x-6\right)=21-\left(5x+3\right)\)
=>\(x-6x+18=21-5x-3\)
=>18=18(luôn đúng)
=>\(x\in R\)
b: \(\left(x-2\right)\left(x+2\right)-\left(x-1\right)^2=2\left(x+1\right)\)
=>\(x^2-4-x^2+2x-1=2x+2\)
=>2x-5=2x+2
=>-7=0(vô lý)
=>\(x\in\varnothing\)
c: \(\dfrac{9x+4}{6}=1-\dfrac{3x-5}{9}\)
=>\(\dfrac{3\left(9x+4\right)}{18}=\dfrac{18}{18}-\dfrac{2\left(3x-5\right)}{18}\)
=>3(9x+4)=18-2(3x-5)
=>27x+12=18-6x+10
=>27x+12=-6x+28
=>33x=16
=>\(x=\dfrac{16}{33}\left(nhận\right)\)
d: ĐKXĐ: \(x\notin\left\{2;5\right\}\)
\(\dfrac{6x+1}{x^2-7x+10}+\dfrac{5}{x-2}=\dfrac{3}{x-5}\)
=>\(\dfrac{6x+1}{\left(x-2\right)\left(x-5\right)}+\dfrac{5}{x-2}=\dfrac{3}{x-5}\)
=>\(6x+1+5\left(x-5\right)=3\left(x-2\right)\)
=>6x+1+5x-25=3x-6
=>11x-24=3x-6
=>8x=18
=>\(x=\dfrac{9}{4}\left(nhận\right)\)
V
26 tháng 1
a: x−3(2x−6)=21−(5x+3)
=>x−6x+18=21−5x−3
=>18=18(luôn đúng)
=>x∈R
b: (x−2)(x+2)−(x−1)2=2(x+1)
=>x2−4−x2+2x−1=2x+2
=>2x-5=2x+2
=>-7=0(vô lý)
=>x∈∅
c: 9x+46=1−3x−59
=>3(9x+4)18=1818−2(3x−5)18
=>3(9x+4)=18-2(3x-5)
=>27x+12=18-6x+10
=>27x+12=-6x+28
=>33x=16
=>x=1633(nhận)
d: ĐKXĐ: x∉{2;5}
6x+1x2−7x+10+5x−2=3x−5
=>6x+1(x−2)(x−5)+5x−2=3x−5
=>6x+1+5(x−5)=3(x−2)6
=>6x+1+5x-25=3x-6
=>11x-24=3x-6
=>8x=18
=>x=94(nhận)
\(\dfrac{2}{x-3}+\dfrac{3}{x+3}=\dfrac{7x+5}{x^2-9}\left(x\ne3;x\ne-3\right)\\ < =>\dfrac{2}{x-3}+\dfrac{3}{x+3}=\dfrac{7x+5}{\left(x-3\right)\left(x+3\right)}\)
suy ra:
`2(x+3)+3(x-3)=7x+5`
`<=>2x+6+3x-9=7x+5`
`<=>2x+3x-7x=5-6+9`
`<=> -2x=8`
`<=> x=-4(tm)`
ĐKXĐ: \(x\ne\pm3\)
\(\dfrac{2}{x-3}+\dfrac{3}{x+3}=\dfrac{7x+5}{x^2-9}\)
\(\Leftrightarrow\dfrac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\dfrac{3\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{7x+5}{\left(x-3\right)\left(x+3\right)}\)
\(\Rightarrow2\left(x+3\right)+3\left(x-3\right)=7x+5\)
\(\Leftrightarrow2x+6+3x-9=7x+5\)
\(\Leftrightarrow2x=-8\)
\(\Leftrightarrow x=-4\) (thỏa)
Vậy pt có nghiệm \(x=-4\)