Tính ,giải giùm mấy man oy =)))
a\(\frac{1}{x^3+3x+2}+\frac{1}{x^2+5x+6}+\frac{1}{x^2+7x+12}+\frac{1}{x^2+9x+20}.\)
b\(\frac{x-1}{x-2}+\frac{1}{2-x}\)
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Những câu hỏi liên quan
28 tháng 7 2017
\(\Leftrightarrow\frac{1}{\left(x-1\right)\left(x-2\right)}+\frac{1}{\left(x-2\right)\left(x-3\right)}+\frac{1}{\left(x-3\right)\left(x-4\right)}+\frac{1}{\left(x-4\right)\left(x-5\right)}=\frac{1}{8}\)
\(\Leftrightarrow\frac{1}{x-1}-\frac{1}{x-2}+\frac{1}{x-2}-\frac{1}{x-3}+...+\frac{1}{x-4}-\frac{1}{x-5}=\frac{1}{8}\)
\(\Leftrightarrow\frac{1}{x-1}-\frac{1}{x-5}=\frac{1}{8}\)
\(\Leftrightarrow\frac{x-5-x+1}{\left(x-1\right)\left(x-5\right)}=\frac{1}{8}\)
\(\Leftrightarrow-4.8=x^2-6x+5\)
\(\Leftrightarrow x^2-6x+37=0\)
JS
26 tháng 2 2020
Sửa đề: x2 + 13x + 41 --> x2 + 13x + 42
Giải:
\(\frac{1}{x^2+3x+2}+\frac{1}{x^2+5x+6}+\frac{1}{x^2+7x+12}+\frac{1}{x^2+9x+20}+\frac{1}{x^2+11x+30}+\frac{1}{x^2+13x+41}=\frac{1}{2}\)
\(\Leftrightarrow\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+4\right)}+\frac{1}{\left(x+4\right)\left(x+5\right)}+\frac{1}{\left(x+5\right)\left(x+6\right)}+\frac{1}{\left(x+6\right)\left(x+7\right)}=\frac{1}{2}\)
(ĐKXĐ: \(x\ne\left\{-1;-2;-3;-4;-5;-6;-7\right\}\))
\(\Leftrightarrow\frac{1}{x+1}-\frac{1}{x+2}+\frac{1}{x+2}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+4}+\frac{1}{x+4}-\frac{1}{x+5}+\frac{1}{x+5}-\frac{1}{x+6}+\frac{1}{x+6}-\frac{1}{x+7}=\frac{1}{2}\)
\(\Leftrightarrow\frac{1}{x+1}-\frac{1}{x+7}=\frac{1}{2}\)
\(\Leftrightarrow\frac{x+7-x-1}{\left(x+1\right)\left(x+7\right)}=\frac{1}{2}\)
\(\Leftrightarrow\left(x+1\right)\left(x+7\right)=12\)
\(\Leftrightarrow x^2+8x+7=12\)
⇔x2-8x=5
⇔ x2-8x+(-4)2=5+(-4)2
⇔ x2-8x+16=21
⇔ (x-4)2=21
⇔ x=±21+4
Vậy...
Chúc bạn học tốt@@
4 tháng 5 2019
ĐKXĐ:\(x\ne1;2;3;4;5\)
\(\Leftrightarrow\frac{1}{x^2-x-2x+2}+\frac{1}{x^2-2x-3x+6}+\frac{1}{x^2-3x-4x+12}+\frac{1}{x^2-4x-5x+20}=\frac{1}{15}\)
\(\Leftrightarrow\frac{1}{\left(x-1\right)\left(x-2\right)}+\frac{1}{\left(x-2\right)\left(x-3\right)}+\frac{1}{\left(x-3\right)\left(x-4\right)}+\frac{1}{\left(x-4\right)\left(x-5\right)}=\frac{1}{15}\)
\(\Leftrightarrow\frac{1}{x-1}-\frac{1}{x-2}+\frac{1}{x-2}-\frac{1}{x-3}+\frac{1}{x-3}-\frac{1}{x-4}+\frac{1}{x-4}-\frac{1}{x-5}=\frac{1}{15}\)
\(\Leftrightarrow\frac{1}{x-1}-\frac{1}{x-5}=\frac{1}{15}\)
\(\Leftrightarrow\frac{15\left(x-5\right)-15\left(x-1\right)}{15\left(x-1\right)\left(x-5\right)}=\frac{\left(x-1\right)\left(x-5\right)}{15\left(x-1\right)\left(x-5\right)}\)
\(\Rightarrow15x-75-15x+15=x^2-6x+5\)
\(\Leftrightarrow x^2-6x+65=0\)
\(\Leftrightarrow\left(x^2-6x+9\right)+56=0\)
\(\Leftrightarrow\left(x-3\right)^2=-56\) (Vô lý)
Vì bình phương một số không thể bằng âm
Vây \(S=\varnothing\)
26 tháng 11 2017
M = 1/(x+1).(x+2) + 1/(x+2).(x+3) + 1/(x+3).(x+4) + 1/(x+4).(x+5) + 1/x+5
= 1/x+1 - 1/x+2 + 1/x+2 - 1/x+3 + 1/x+3 - 1/x+4 + 1/x+4 - 1/x+5 + 1/x+5 = 1/x+1
k mk nha
7 tháng 11 2017
pt <=> 1/(x+2).(x+3) + 1/(x+3).(x+4) + 1/(x+4).(x+5) + 1/(x+5).(x+6) = 1/8
<=> 1/x+2 - 1/x+3 + 1/x+3 - 1/x+4 + 1/x+4 - 1/x+5 + 1/x+5 - 1/x+6 = 1/8
<=> 1/x+2 - 1/x+6 = 1/8
<=> (x+6-x-2)/(x+2).(x+6) = 1/8
<=> 4/(x+2).(x+6) = 1/8
<=>(x+2).(x+6) = 4 : 1/8 = 32
<=>x^2 + 8x + 12 = 32
<=> x^2+8x+12-32=0
<=>x^2+8x-20=0
<=>(x-2).(x+10)=0
<=> x-2 =0 hoặc x+10 = 0
<=> x=2 hoặc x=-10
28 tháng 12 2019
giang sinh an lanh $%###Xuyen gam cu chuoi###%$
29 tháng 11 2017
\(\Rightarrow\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+4\right)}+\frac{1}{\left(x+4\right)\left(x+5\right)}=\frac{1}{6}\)
ĐK:\(x\ne-2;-3;-4;-5\)
MTC:\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right).6\)
Quy đồng khử mẫu:
b,
đổi dấu
-(x-1)/2-x +1/2-x
=-x+1+1/2-x
=2-x/2-x
=1
Thặc vler .V
A/\(\frac{1}{x^2+3x+2}+\frac{1}{x^2+5x+6}+\frac{1}{x^2+7x+12}+\frac{1}{x^2+9x+20}\)
\(=\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+4\right)}+\frac{1}{\left(x+4\right)\left(x+5\right)}\)
\(=\left[\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}\right]+\left[\frac{1}{\left(x+3\right)\left(x+4\right)}+\frac{1}{\left(x+4\right)\left(x+5\right)}\right]\)
\(=\left[\frac{x+3}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}+\frac{x+1}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}\right]+\left[\frac{x+5}{\left(x+3\right)\left(x+4\right)\left(x+5\right)}+\frac{x+3}{\left(x+3\right)\left(x+4\right)\left(x+5\right)}\right]\)
\(=\frac{2x+4}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}+\frac{2x+8}{\left(x+3\right)\left(x+4\right)\left(x+5\right)}\)
\(=\frac{2\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}+\frac{2\left(x+4\right)}{\left(x+3\right)\left(x+4\right)\left(x+5\right)}\)
\(=\frac{2}{\left(x+1\right)\left(x+3\right)}+\frac{2}{\left(x+3\right)\left(x+5\right)}\)
\(=\frac{2x+10}{\left(x+1\right)\left(x+3\right)\left(x+5\right)}+\frac{2x+2}{\left(x+1\right)\left(x+3\right)\left(x+5\right)}\)
\(=\frac{4x+12}{\left(x+1\right)\left(x+3\right)\left(x+5\right)}\)
\(=\frac{4\left(x+3\right)}{\left(x+1\right)\left(x+3\right)\left(x+5\right)}\)
\(=\frac{4}{\left(x+1\right)\left(x+5\right)}\)
B/\(\frac{x-1}{x-2}+\frac{1}{2-x}\)
\(=\frac{x-1}{x-2}-\frac{1}{x-2}\)
\(=\frac{x-1-1}{x-2}\)
\(=\frac{x-2}{x-2}\)
\(=1\)