Giải PT:
a) \(\frac{2}{x^2+4x+3}+\frac{5}{x^2+11x+24}+\frac{2}{x^2+18x+80}=\frac{9}{52}\)
b) \(x^2+\left(\frac{x}{x+1}\right)^2=\frac{5}{4}\)
c) \(x^4-3x^3+2x^2-9x+9=0\)
Giải PT:
a) \(\frac{2}{x^2+4x+3}+\frac{5}{x^2+11x+24}+\frac{2}{x^2+18x+80}=\frac{9}{52}\)
b) \(x^2+\left(\frac{x}{x+1}\right)^2=\frac{5}{4}\)
c) \(x^4-3x^3+2x^2-9x+9=0\)
a) \(ĐKXĐ:x\ne-1;x\ne-3;x\ne-8;x\ne-10\)
\(\frac{2}{x^2+4x+3}+\frac{5}{x^2+11x+24}+\frac{2}{x^2+18x+8x}=\frac{9}{52}\)
\(\Leftrightarrow\frac{2}{\left(x+1\right)\left(x+3\right)}+\frac{5}{\left(x+3\right)\left(x+8\right)}+\frac{2}{\left(x+10\right)\left(x+8\right)}-\frac{9}{52}=0\)
\(\Leftrightarrow\frac{104\left(x+10\right)\left(x+8\right)+260\left(x+1\right)\left(x+10\right)+104\left(x+1\right)\left(x+3\right)-9\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
Đoạn này cậu tự phân tích tử rồi rút gọn nhé :D Vì hơi dài nên viết ra đây sẽ rối, k đẹp mắt cho lắm :>
\(\Leftrightarrow\frac{-927x^2+1782x+9072-9x^4-198x^3}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
\(\Leftrightarrow\frac{-9\left(x^4+22x^3+103x^2-198x-1008\right)}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
\(\Leftrightarrow\frac{-9\left(x^4-3x^3+25x^3-75x^{^2}+178x^2-534x+336x-1008\right)}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
\(\Leftrightarrow\frac{-9\left[x^3\left(x-3\right)+25x^2\left(x-3\right)+178x\left(x-3\right)+336\left(x-3\right)\right]}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
\(\Leftrightarrow\frac{-9\left(x-3\right)\left(x^3+25x^2+178x+336\right)}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
\(\Leftrightarrow\frac{-9\left(x-3\right)\left(x^3+14x^2+11x^2+154x+24x+336\right)}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
\(\Leftrightarrow\frac{-9\left(x-3\right)\left[x^2\left(x+14\right)+11x\left(x+14\right)+24\left(x+14\right)\right]}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
\(\Leftrightarrow\frac{-9\left(x-3\right)\left(x+14\right)\left(x^2+11x+24\right)}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)=0}\)
\(\Leftrightarrow\frac{-9\left(x+14\right)\left(x-3\right)\left(x+3\right)\left(x+8\right)}{52\left(x+1\right)\left(x+3\right)\left(x+8\right)\left(x+10\right)}=0\)
\(\Leftrightarrow\frac{-9\left(x+14\right)\left(x-3\right)}{52\left(x+1\right)\left(x+10\right)}=0\)
\(\Leftrightarrow-9x^2-99x+378=0\)
\(\Leftrightarrow x^2+11x-42=0\)
\(\Leftrightarrow\left(x+14\right)\left(x-3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+14=0\\x-3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-14\\x=3\end{cases}}}\)
Vậy tập nghiệm của phương trình là : \(S=\left\{-14;3\right\}\)
b) \(ĐKXĐ:x\ne-1\)
\(x^2+\left(\frac{x}{x+1}\right)^2=\frac{5}{4}\)
\(\Leftrightarrow x^2+\frac{x^2}{\left(x+1\right)^2}-\frac{5}{4}=0\)
\(\Leftrightarrow\frac{4x^2\left(x^2+2x+1\right)+4x^2-5\left(x^2+2x+1\right)}{\left(x+1\right)^2}=0\)
\(\Leftrightarrow4x^4+8x^3+4x^2+4x^2-5x^2-10x-5=0\)
\(\Leftrightarrow4x^2+8x^3+3x^2-10x-5=0\)
\(\Leftrightarrow4x^4+2x^3+6x^3+3x^2-10x-5=0\)
\(\Leftrightarrow2x^3\left(2x+1\right)+3x^2\left(2x+1\right)-5\left(2x+1\right)=0\)
\(\Leftrightarrow\left(2x+1\right)\left(2x^3+3x^2-5\right)=0\)
\(\Leftrightarrow\left(2x+1\right)\left(2x^3-2x^2+5x^2-5x+5x-5\right)=0\)
\(\Leftrightarrow\left(2x+1\right)\left[2x^2\left(x-1\right)+5x\left(x-1\right)+5\left(x-1\right)\right]=0\)
\(\Leftrightarrow\left(2x+1\right)\left(x-1\right)\left(2x^2+5x+5\right)=0\)
\(\Leftrightarrow2x+1=0\)
hoặc \(x-1=0\)
hoặc \(2x^2+5x+5=0\)
\(\Leftrightarrow\) \(x=-\frac{1}{2}\left(tm\right)\)
hoặc \(x=1\left(tm\right)\)
hoặc \(\left(x+\frac{5}{4}\right)^2+\frac{55}{16}=0\left(ktm\right)\)
Vậy tập nghiệm của phương trình là : \(S=\left\{-\frac{1}{2};1\right\}\)
c) \(x^4-3x^3+2x^2-9x+9=0\)
\(\Leftrightarrow x^4-x^3-2x^3+2x^2-9x+9=0\)
\(\Leftrightarrow x^3\left(x-1\right)-2x^2\left(x-1\right)-9\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^3-2x^2-9\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[\left(x^3-3x^2\right)+\left(x^2-9\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left[x^2\left(x-3\right)+\left(x-3\right)\left(x+3\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-3\right)\left(x^2+x+3\right)=0\)
\(\Leftrightarrow\)\(x-1=0\)
hoặc \(x-3=0\)
hoặc \(x^2+x+3=0\)
\(\Leftrightarrow\)\(x=1\left(tm\right)\)
hoặc \(x=3\left(tm\right)\)
hoặc \(\left(x-\frac{1}{2}\right)^2+\frac{11}{4}=0\left(ktm\right)\)
Vậy tập nghiệm của phương trình là :\(S=\left\{1;3\right\}\)
\(ĐKXĐ:x\ne-1;x\ne-3;x\ne-8;x\ne-10\)
\(pt\Leftrightarrow\frac{2}{\left(x+1\right)\left(x+3\right)}+\frac{5}{\left(x+3\right)\left(x+8\right)}+\frac{2}{\left(x+8\right)\left(x+10\right)}=\frac{9}{52}\)
\(\Leftrightarrow\frac{\left(x+3\right)-\left(x+1\right)}{\left(x+1\right)\left(x+3\right)}+\frac{\left(x+8\right)-\left(x+3\right)}{\left(x+3\right)\left(x+8\right)}+\frac{\left(x+10\right)-\left(x+8\right)}{\left(x+8\right)\left(x+10\right)}\)
\(=\frac{9}{52}\)
\(\Leftrightarrow\frac{1}{x+1}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+8}+\frac{1}{x+8}-\frac{1}{x+10}=\frac{9}{52}\)
\(\Leftrightarrow\frac{1}{x+1}-\frac{1}{x+10}=\frac{9}{52}\)
\(\Leftrightarrow\frac{9}{\left(x+1\right)\left(x+10\right)}=\frac{9}{52}\)
\(\Leftrightarrow\left(x+1\right)\left(x+10\right)=52\)
\(\Leftrightarrow x^2+11x+10=52\)
\(\Leftrightarrow x^2+11x-42=0\)
\(\Delta=11^2+4.42=289,\sqrt{289}=17\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{-11+17}{2}=3\\x=\frac{-11-17}{2}=-14\end{cases}}\)
Vậy pt có 2 nghiệm là 3 và -14
战哥làm dài và khó hiểu))):????
1, giải pt sau
a,\(\frac{9}{x}+2=-6\)
b,\(\frac{7}{x+1}+\frac{-18x}{x\left(x^2+4x+3\right)}=\frac{-4}{x+3}\)
c,\(\frac{3x-1}{x-1}-1=\frac{2x+5}{x+3}+\frac{4}{x^2+2x-3}\)
a) ĐKXĐ: x≠0
Ta có: \(\frac{9}{x}+2=-6\)
⇔\(\frac{9}{x}+2+6=0\)
⇔\(\frac{9}{x}+8=0\)
⇔\(\frac{9}{x}+\frac{8x}{x}=0\)
⇔9+8x=0
⇔8x=-9
hay \(x=-\frac{9}{8}\)
Vậy: \(x=-\frac{9}{8}\)
b) ĐKXĐ: x≠0;x≠-1;x≠-3
Ta có: \(\frac{7}{x+1}+\frac{-18x}{x\left(x^2+4x+3\right)}=\frac{-4}{x+3}\)
⇔\(\frac{7}{x+1}+\frac{-18x}{x\left(x+1\right)\left(x+3\right)}-\frac{-4}{x+3}=0\)
⇔\(\frac{7x\left(x+3\right)}{\left(x+1\right)\cdot x\cdot\left(x+3\right)}+\frac{-18x}{\left(x+1\right)\cdot x\cdot\left(x+3\right)}-\frac{-4x\left(x+1\right)}{\left(x+3\right)\cdot x\cdot\left(x+1\right)}=0\)
⇔\(7x^2+21x-18x+4x\left(x+1\right)=0\)
\(\Leftrightarrow7x^2+21x-18x+4x^2+4x=0\)
⇔\(11x^2+7x=0\)
\(\Leftrightarrow x\left(11x+7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\11x+7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\11x=-7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=\frac{-7}{11}\end{matrix}\right.\)
Vậy: \(x=\frac{-7}{11}\)
c) ĐKXĐ: x≠1; x≠-3
Ta có: \(\frac{3x-1}{x-1}-1=\frac{2x+5}{x+3}+\frac{4}{x^2-2x+3}\)
⇔\(\frac{3x-1}{x-1}-1-\frac{2x+5}{x+3}-\frac{4}{\left(x-1\right)\left(x+3\right)}=0\)
⇔\(\frac{\left(3x-1\right)\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}-\frac{\left(x-1\right)\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}-\frac{\left(2x+5\right)\left(x-1\right)}{\left(x+3\right)\left(x-1\right)}-\frac{4}{\left(x-1\right)\left(x+3\right)}=0\)
⇔\(\left(3x-1\right)\left(x+3\right)-\left(x-1\right)\left(x+3\right)-\left(2x+5\right)\left(x-1\right)-4=0\)
\(\Leftrightarrow3x^2+9x-x-3-\left(x^2+3x-x-3\right)-\left(2x^2-2x+5x-5\right)-4=0\)
\(\Leftrightarrow3x^2+8x-3-\left(x^2+2x-3\right)-\left(2x^2+3x-5\right)-4=0\)
\(\Leftrightarrow3x^2+8x-3-x^2-2x+3-2x^2-3x+5-4=0\)
\(\Leftrightarrow3x+1=0\)
\(\Leftrightarrow3x=-1\)
hay \(x=\frac{-1}{3}\)
Vậy: \(x=\frac{-1}{3}\)
Giải phương trình sau
\(\frac{2}{x^2+4x+3}+\frac{5}{x^2+11x+24}+\frac{2}{x^2+18x+80}=\frac{9}{52}\)
ĐKXĐ: \(x\ne\left\{-10;-8;-3;-1\right\}\)
\(\frac{2}{\left(x+1\right)\left(x+3\right)}+\frac{5}{\left(x+3\right)\left(x+8\right)}+\frac{2}{\left(x+8\right)\left(x+10\right)}=\frac{9}{52}\)
\(\Leftrightarrow\frac{1}{x+1}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+8}+\frac{1}{x+8}-\frac{1}{x+10}=\frac{9}{52}\)
\(\Leftrightarrow\frac{1}{x+1}-\frac{1}{x+10}=\frac{9}{52}\)
\(\Leftrightarrow\frac{9}{\left(x+1\right)\left(x+10\right)}=\frac{9}{52}\)
\(\Leftrightarrow\left(x+1\right)\left(x+10\right)=52\)
\(\Leftrightarrow x^2+11x-42=0\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-14\end{matrix}\right.\)
bài 1:giải các pt sau:
a/\(\frac{1-x}{x+1}\)+3=\(\frac{2x+3}{x+1}\)
b/\(\frac{\left(x+2\right)^2}{2x-3}-1=\frac{x^2+10}{2x-3}\)
c/\(\frac{1}{x+1}-\frac{5}{x-2}=\frac{15}{\left(x+1\right)\left(2-x\right)}\)
d/\(\frac{1-6x}{x-2}+\frac{9x+4}{x+2}=\frac{x\left(3x-2\right)+1}{x^2-4}\)
e/\(\frac{12}{1-9x^2}=\frac{1-3x}{1+3x}-\frac{1+3x}{1-3x}\)
f\(\frac{x+4}{x^2-3x+2}+\frac{x+1}{x^2-4x+3}=\frac{2x+5}{x^2-4x+3}\)
bài tập. Giải các pt
1, \(\frac{5}{x-2}+\frac{6}{3-4x}=0\)
2,\(\frac{x+1}{x-2}=\frac{1}{x^2-4}\)
3,\(\frac{x+2}{x}-\frac{x^2+5x+4}{x\left(x+2\right)}=\frac{x}{x+2}\)
4,\(\frac{1-6x}{x-2}+\frac{9x+4}{x+2}=\frac{x\left(3x-2\right)+1}{x^2-4}\)
5,\(\frac{3x+2}{3x-2}-\frac{6}{2+3x}=\frac{9x^2}{9x^2-4}\)
6,\(\frac{x+1}{x}+\frac{1}{x+1}=\frac{2x-1}{2x^2+2}\)
7,\(\frac{2}{x+1}-\frac{3x+1}{\left(x+1\right)}=\frac{1}{\left(x+1\right)\left(x-2\right)}\)
8,\(\frac{4}{x^2+2x-3}=\frac{2x-5}{x+3}-\frac{2x}{x-1}\)
9,\(\frac{3}{x^2+x-2}-\frac{1}{x-1}=\frac{-7}{x+2}\)
ĐKXĐ : \(\hept{\begin{cases}x-2\ne0\\3-4x\ne0\end{cases}\Rightarrow\hept{\begin{cases}x\ne2\\x\ne\frac{3}{4}\end{cases}}}\)
\(\frac{5}{x-2}+\frac{6}{3-4x}=0\)
\(\frac{5\left(3-4x\right)}{\left(x-2\right)\left(3-4x\right)}+\frac{6\left(x-2\right)}{\left(3-4x\right)\left(x-2\right)}=0\)
\(15-20x+6x-12=0\)
\(3-14x=0\Leftrightarrow14x=3\Leftrightarrow x=\frac{3}{14}\)theo ĐKXĐ : x thỏa mãn
Giải các phương trình sau:
a) \(\frac{4}{x-1}-\frac{5}{x-2}=-3\)
b) \(3x-\frac{1}{x-2}=\frac{x-1}{2-x}\)
c) \(\frac{x+4}{x^2-3x+2}+\frac{x+1}{x^2-4x+3}=\frac{2x+5}{x^2-4x+3}\)
d) \(\frac{2}{x^2-4}-\frac{1}{x\left(x-2\right)}+\frac{x-4}{x\left(x+2\right)}=0\)
e) \(\frac{4x}{x^2+4x+3}-1=6\left(\frac{1}{x+3}-\frac{1}{2x+2}\right)\)
f) \(\frac{3}{4\left(x-5\right)}+\frac{15}{50-2x^2}=\frac{7}{6x+30}\)
g)\(\frac{1}{x-1}+\frac{2x^2-5}{x^3-1}=\frac{4}{x^2+x+1}\)
h) \(\frac{12x+1}{6x-2}-\frac{9x-5}{3x+1}=\frac{108x-36x^2-9}{4\left(9x^2-1\right)}\)
i) \(x+\frac{1}{x}=x^2+\frac{1}{x^2}\)
j) \(\frac{1}{x}+2=\left(\frac{1}{x}+2\right)\left(x^2+2\right)\)
k) \(\left(x+1+\frac{1}{x}\right)^2=\left(x-1-\frac{1}{x}\right)^2\)
Dạng 1: Phương trình bậc nhất
Bài 1: Giải các phương trình sau :
a) 0,5x (2x - 9) = 1,5x (x - 5)
b) 28 (x - 1) - 9 (x - 2) = 14x
c) 8 (3x - 2) - 14x = 2 (4 - 7x) + 18x
d) 2 (x - 5) - 6 (1 - 2x) = 3x + 2
e) \(\frac{x+7}{2}-\frac{x-3}{5}=\frac{x}{6}\)
f) \(\frac{2x-3}{3}-\frac{5x+2}{12}=\frac{x-3}{4}+1\)
g) \(\frac{x+6}{2}+\frac{2\left(x+17\right)}{2}+\frac{5\left(x-10\right)}{6}=2x+6\)
h) \(\frac{3x+2}{5}-\frac{4x-3}{7}=4+\frac{x-2}{35}\)
i) \(\frac{x-1}{2}+\frac{x+3}{3}=\frac{5x+3}{6}\)
j) \(\frac{x-3}{5}-1=\frac{4x+1}{4}\)
Dạng 2: Phương trình tích
Bài 2: Giải phương trình sau :
a) (x + 1) (5x + 3) = (3x - 8) (x - 1)
b) (x - 1) (2x - 1) = x(1 - x)
c) (2x - 3) (4 - x) (x - 3) = 0
d) (x + 1)2 - 4x2 = 0
e) (2x + 5)2 = (x + 3)2
f) (2x - 7) (x + 3) = x2 - 9
g) (3x + 4) (x - 4) = (x - 4)2
h) x2 - 6x + 8 = 0
i) x2 + 3x + 2 = 0
j) 2x2 - 5x + 3 = 0
k) x (2x - 7) - 4x + 14 = 9
l) (x - 2)2 - x + 2 = 0
Dạng 3: Phương trình chứa ẩn ở mẫu
Bài 3: Giải phương trình sau :
\(\frac{90}{x}-\frac{36}{x-6}=2\) | \(\frac{3}{x+2}-\frac{2}{x-3}=\frac{8}{\left(x-3\right)\left(x+2\right)}\) |
\(\frac{1}{x}+\frac{1}{x+10}=\frac{1}{12}\) | \(\frac{1}{2x-3}-\frac{3}{x\left(2x-3\right)}=\frac{5}{x}\) |
\(\frac{x+3}{x-3}-\frac{1}{x}=\frac{3}{x\left(x-3\right)}\) | \(\frac{3}{4\left(x-5\right)}+\frac{15}{50-2x^2}=\frac{-7}{6\left(x+5\right)}\) |
\(\frac{3}{x+2}-\frac{2}{x-2}+\frac{8}{x^2-4}=0\) | \(\frac{x}{x+1}-\frac{2x-3}{1-x}=\frac{3x^2+5}{x^2-1}\) |
Giải phương trình:
a, \(\frac{1}{2}\left(x+1\right)+\frac{1}{4}\left(x+3\right)=3-\frac{1}{3}\left(x+2\right)\)
b, \(\frac{x+\frac{2\left(3-x\right)}{5}}{14}-\frac{5x-4\left(x-1\right)}{24}=\frac{7x+2+\frac{9-3x}{5}}{12}+\frac{2}{3}\)
c,3(x-1)(2x-1)=5(x+8)(x-1)
d, \(9x^2-1=\left(3x+1\right)\left(4x+1\right)\)
bài 1 giải phương trình
a) (2x+3)\(^2\)-3(x-4)(x+4)=\(\left(x-2\right)^2\)+1
b)(3x-2) (9x\(^2\)+6x+4)-(3x-1) (9x\(^2\)+3x+1)=x-4
c)x (x-1) -(x-3) (x+4)=5x
d) (2x+1)(2x-1)=4x(x-7)-3x
bài 2 giải phương trình
a)\(\frac{x}{10}-\left(\frac{x}{30}+\frac{2x}{45}\right)=\frac{4}{5}\)
b)\(\frac{10x-5}{18}+\frac{x+3}{12}=\frac{7x+3}{6}+\frac{12-x}{9}\)
c)\(\frac{10x+3}{8}=\frac{7-8x}{12}\)
d)\(\frac{x+4}{5}-x-5=\frac{x+3}{3}-\frac{x-2}{2}\)