a) \(\frac{4}{x+5}=\frac{3}{x-4}\)
=> 4.(x - 4) = 3.(x + 5)
=> 4x - 16 = 3x + 15
=> 4x - 3x = 15 + 16
=> 1x = 31
=> x = 31 : 1
=> x = 31
Vậy x = 31.
b) \(5-\frac{2}{x}=\frac{3}{-7}\)
=> \(\frac{2}{x}=5-\frac{-3}{7}\)
=> \(\frac{2}{x}=\frac{38}{7}\)
=> 2 . 7 = 38 . x
=> 14 = 38 . x
=> x = 14 : 38
=> x = \(\frac{14}{38}=\frac{7}{19}\)
Vậy x = \(\frac{7}{19}\).
e) \(\frac{x}{7}=-\frac{15}{14}\)
=> x . 14 = (-15) . 7
=> x . 14 = -105
=> x = (-105) : 14
=> x = \(-7,5=-\frac{15}{2}\)
Vậy x = \(-\frac{15}{2}\).
f) 2 - (2x + 3) = 7
=> 2x + 3 = 2 - 7
=> 2x + 3 = -5
=> 2x = (-5) - 3
=> 2x = -8
=> x = (-8) : 2
=> x = -4
Vậy x = -4.
Chúc bạn học tốt!
a, ĐK: \(x\ne-5;4\)
pt\(\Rightarrow4x-16=3x+15\)
\(\Leftrightarrow x=31\left(TM\right)\)
Ttự các câu còn lại.
a/\(\frac{4}{x+5}=\frac{3}{x-4}\)
⇔\(\frac{4\left(x+4\right)}{\left(x+5\right)\left(x+4\right)}=\frac{3\left(x+5\right)}{\left(x+4\right)\left(x+5\right)}\)
➞ \(4x+16=3x+15\)
⇔\(4x-3x=15-16\)
⇔\(x=-1\)
Vậy S={-1}
b/\(5-\frac{2}{x}=\frac{3}{-7}\)
⇔\(\frac{5.\left(-7x\right)}{-7x}\) \(-\frac{2.\left(-7\right)}{x.\left(-7\right)}\)=\(\frac{3.x}{-7.x}\)
➞\(-35x+14=3x\)
⇔\(-35x-3x=-14\)
⇔\(-38x=-14\)
⇔\(x=\frac{7}{19}\)
Vậy S={\(\frac{7}{19}\)}
c/ \(\frac{x+5}{6}-4=\frac{5}{2}\)
⇔\(\frac{x+5}{6}-\frac{4.6}{6}=\frac{5.3}{6}\)
➝\(x+5-24=15\)
⇔\(x-19=15\)
⇔\(x=15+19\)
⇔\(x=34\)
Vậy x=34
d/\(8-\frac{7}{x+4}=\frac{5}{2}\)
⇔\(\frac{8.2\left(x+4\right)}{2\left(x+4\right)}-\frac{7.2}{\left(x+4\right).2}=\frac{5\left(x+4\right)}{2\left(x+4\right)}\)
➞\(16x+64-14=5x+20\)
⇔\(16x-5x=20-50\)
⇔\(11x=-30\)
⇔\(x=\frac{-30}{11}\)
Vậy S={ \(\frac{-30}{11}\)}
e/\(\frac{x}{7}=\frac{-15}{14}\)
⇔ \(\frac{2x}{14}=\frac{-15}{14}\)
➜\(2x=-15\)
⇔ \(x=\frac{-15}{2}\)
Vậy S={\(\frac{-15}{2}\)}
f/\(2-\left(2x+3\right)=7\)
⇔ 2 - 2x -3 =7
⇔ 2 -3-7= 2x
⇔ -8=2x
⇔\(x=-4\)
Vậy S={-4}
a, \(\frac{4}{x+5}=\frac{3}{x-4}=>4.\left(x-4\right)=3.\left(x+5\right)\)
=> 4x - 16 = 3x + 15
=> 4x -3x = 15 + 16
x = 31
b, \(5-\frac{2}{x}=\frac{3}{-7}=>\frac{2}{x}=5-\frac{3}{-7}\)
=> \(\frac{2}{x}=\frac{38}{7}\) => 2.7 = 38.x
=> 14 = 38.x
x = 14 : 38
x = \(\frac{7}{19}\)
c, \(\frac{x+5}{6}-4=\frac{5}{2}=>\frac{x+5}{6}=\frac{13}{2}\)
=> (x+5).2=13.6
=> 2x + 10 = 78
=> 2x = 68
x = 68 : 2 = 34
d, \(8-\frac{7}{x+4}=\frac{5}{2}=>\frac{7}{x+4}=\frac{11}{2}\)
=> 14 = ( x + 4 ) . 11
=> 14 = 11x + 44
11x = 14 - 44
11x = -30
x = \(\frac{-30}{11}\)
e, \(\frac{x}{7}=\frac{-15}{14}=>x.14=7.-15\)
=> 14x = 105
x = -105 : 14
x = \(\frac{-15}{2}\)
f, 2 - ( 2x + 3 ) = 7
=> 2x + 3 = 2 - 7
2x + 3 = -5
2x = -5 - 3
2x = -8
x = -4
