(3/4)x = 28/34
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a: =197+3*(34-64)
=197-3*30
=197-90=107
b: =25(134-34)+100=100*26=2600
d: =>x thuộc B(84)
mà 100<x<200
nên x=168
A) \(\frac{7}{\left(x+3\right)\left(x+10\right)}+\frac{11}{\left(x+10\right)\left(x+21\right)}+\frac{13}{\left(x+21\right)\left(x+34\right)}\)
\(=\frac{\left(x+10\right)-\left(x+3\right)}{\left(x+3\right)\left(x+10\right)}+\frac{\left(x+21\right)-\left(x+10\right)}{\left(x+10\right)\left(x+21\right)}+\frac{\left(x+34\right)-\left(x+21\right)}{\left(x+21\right)\left(x+34\right)}\)
\(=\frac{1}{x+3}-\frac{1}{x+10}+\frac{1}{x+10}-\frac{1}{x+21}+\frac{1}{x+21}-\frac{1}{x+34}\)
\(=\frac{1}{x+3}-\frac{1}{x+34}\)
\(=\frac{\left(x+34\right)-\left(x+3\right)}{\left(x+3\right)\left(x+34\right)}\)\(=\frac{x}{\left(x+3\right)\left(x+34\right)}\)
\(\Rightarrow\left(x+34\right)-\left(x+3\right)=x\)
\(\Rightarrow x=31\)
Vậy, x = 31
Bạn áp dụng: \(\frac{k}{x\cdot\left(x+k\right)}=\frac{1}{x}-\frac{1}{x+k}\) với \(x,k\inℝ;x\ne0;x\ne-k\)
Chứng minh: \(\frac{1}{x}-\frac{1}{x+k}=\frac{x+k}{x\left(x+k\right)}-\frac{x}{x\left(x+k\right)}=\frac{x+k-x}{x\left(x+k\right)}=\frac{k}{x\left(x+k\right)}\)
\(a,71-3(12-x)=125\\3(12-x)=71-125\\3(12-x)=-54\\12-x=-54:3\\12-x=-18\\x=12-(-18)\\x=30\\---\)
\(b,3(12+x)-41=-50\\3(12+x)=-50+41\\3(12+x)=-9\\12+x=-9:3\\12+x=-3\\x=-3-12\\x=-15\\---\)
\((14+2x)-34=-28\\14+2x=-28+34\\14+2x=6\\2x=6-14\\2x=-8\\x=-8:2\\x=-4\\Toru\)
3(12 - x) = 71 - 125
3(12 - x) = -54
12 - x = -54 : 3
12 -x = -18
x = 12 + 18
x = 30
b) 3(12+x)- 41= -50
3(12 + x) = -50 + 41
3(12 - x) = -9
12 - x = -9 : 3
12 - x = -3
x = 12 + 3
x = 15
c)(14+2x)-34=-28
( 14 + 2x) = -28 + 34
(14 + 2x) = 6
2x = 6 - 14
2x = -8
x = -8 : 2
x = -4
--thonezz--
\(\left(\frac{3}{4}\right)^x=\frac{2^8}{3^4}\Leftrightarrow\frac{3^x}{4^x}=\frac{2^8}{3^4}\)
\(\Leftrightarrow3^x.3^4=2^8.4^x\Leftrightarrow3^{x+4}=\left(2^2\right)^4.4^x\)
\(\Leftrightarrow3^{x+4}=4^{4+x}\Leftrightarrow3^{x+4}-4^{x+4}=0\)xD