Khi giải phương trình :
\(\dfrac{2-3x}{-2x-3}=\dfrac{3x+2}{2x+1}\)
bạn Hà làm như sau :
Theo định nghĩa hai phân thức bằng nhau, ta có :
\(\dfrac{2-3x}{-2x-3}=\dfrac{3x+2}{2x+1}\Leftrightarrow\left(2-3x\right)\left(2x+1\right)=\left(3x+2\right)\left(-2x-3\right)\)
\(\Leftrightarrow-6x^2+x+2=-6x^2-13x-6\)
\(\Leftrightarrow x=-\dfrac{4}{7}\)
Vậy phương trình có nghiệm \(x=-\dfrac{4}{7}\)
Giải các phương trình sau :
a) \(\dfrac{1-x}{x+1}+3=\dfrac{2x+3}{x+1}\)
b) \(\dfrac{\left(x+2\right)^2}{2x-3}-1=\dfrac{x^2+10}{2x-3}\)
c) \(\dfrac{5x-2}{2-2x}+\dfrac{2x-1}{2}=1-\dfrac{x^2+x-3}{1-x}\)
d) \(\dfrac{5-2x}{3}+\dfrac{\left(x-1\right)\left(x+1\right)}{3x-1}=\dfrac{\left(x+2\right)\left(1-3x\right)}{9x-3}\)
Giải các phương trình sau :
a) \(\dfrac{1-6x}{x-2}+\dfrac{9x+4}{x+2}=\dfrac{x\left(3x-2+1\right)}{x^2-4}\)
b) \(1+\dfrac{x}{3-x}=\dfrac{5x}{\left(x+2\right)\left(3-x\right)}+\dfrac{2}{x+2}\)
c) \(\dfrac{2}{x-1}+\dfrac{2x+3}{x^2+x+1}=\dfrac{\left(2x-1\right)\left(2x+1\right)}{x^3-1}\)
d) \(\dfrac{x^3-\left(x-1\right)^3}{\left(4x+3\right)\left(x-5\right)}=\dfrac{7x-1}{4x+3}-\dfrac{x}{x-5}\)
1) \(\dfrac{7x-3}{x-1}\) = \(\dfrac{2}{3}\)
2) \(\dfrac{2\left(3-7x\right)}{1+x}\) = \(\dfrac{1}{2}\)
3) \(\dfrac{x^{2^{ }}-6}{x}\) = x + \(\dfrac{3}{2}\)
4) \(\dfrac{5}{3x+2}\) = 2x - 1
5) \(\dfrac{\left(x^2+2x\right)-\left(3x+6\right)}{x-3}\) = 0
6) \(\dfrac{1}{x-2}\) + 3 = \(\dfrac{3-x}{x-2}\)
Giải các phương trình :
a) \(\dfrac{1}{x-1}-\dfrac{3x^2}{x^3-1}=\dfrac{2x}{x^2+x+1}\)
b) \(\dfrac{3}{\left(x-1\right)\left(x-2\right)}+\dfrac{2}{\left(x-3\right)\left(x-1\right)}=\dfrac{1}{\left(x-2\right)\left(x-3\right)}\)
c) \(1+\dfrac{1}{x+2}=\dfrac{12}{8+x^3}\)
d) \(\dfrac{13}{\left(x-3\right)\left(2x+7\right)}+\dfrac{1}{2x+7}=\dfrac{6}{\left(x-3\right)\left(x+3\right)}\)
\(a,\dfrac{3\left(2x+1\right)}{4}-5-\dfrac{3x+2}{10}=\dfrac{2\left(3x-1\right)}{5}\)
b,\(\dfrac{x-15}{23}+\dfrac{x-23}{15}-2=0\)
c,\(\dfrac{3\left(2x+1\right)}{4}-\dfrac{5x+3}{6}+\dfrac{x+1}{3}=x+\dfrac{7}{12}\)
Giải các phương trình
a) \(\dfrac{2x-5}{x+5}=3\)
b) \(\dfrac{x^2-6}{x}=x+\dfrac{3}{2}\)
c) \(\dfrac{\left(x^2+2x\right)-\left(3x+6\right)}{x-3}=0\)
d) \(\dfrac{5}{3x+2}=2x-1\)
Giải pt: \(\dfrac{3}{5x-1}+\dfrac{2}{3-5x}=\dfrac{4}{\left(1-5x\right)\left(x-3\right)}\)
\(\dfrac{5+96}{x^2-16}=\dfrac{2x—1}{x+4}-\dfrac{3x-1}{4-x}\)
Giúp mk nha
Giải các phương trình
1/ \(\dfrac{1}{x^2+3x+2}+\dfrac{1}{x^2+5x+6}+\dfrac{1}{x^2+7x+12}=\dfrac{1}{6}\)
2/ \(\dfrac{1}{x^2-6x+8}+\dfrac{1}{x^2-10x+24}+\dfrac{1}{x^2-14x+48}=\dfrac{1}{9}\)
3/ \(\dfrac{1}{x^2-3x+3}+\dfrac{2}{x^2-3x+4}=\dfrac{6}{x^2-3x+5}\)
4/ \(\dfrac{6}{\left(x+1\right)\left(x+2\right)}+\dfrac{8}{\left(x-1\right)\left(x+4\right)}=1\)
5/ \(4\left(x^3+\dfrac{1}{x^3}\right)=13\left(x+\dfrac{1}{x}\right)\)
6/ \(\dfrac{4x}{4x^2-8x+7}+\dfrac{3x}{4x^2-10x+7}=1\)
7/ \(\dfrac{x^2-3x+5}{x^2-4x+5}-\dfrac{x^2-5x+5}{x^2-6x+5}=-\dfrac{1}{4}\)
8/ \(x.\dfrac{8-x}{x-1}\left(x-\dfrac{8-x}{x-1}\right)=15\)
giải các bất pt sau:
a, 4x-10<0
b, 2x+x+12\(\ge0\)
c, x-5\(\ge3-x\)
d, 7-3x>9-x
đ, 2x-(3-5x)\(\le4\left(x+3\right)\)
e, 3x-6+x<9-x
f, 2t-3+5t\(\ge\)4t+12
g, 3y-2\(\le2y-3\)
h,3-4x+24+6x\(\ge x+27+3x\)
i, 5-(6-x)\(\le4\left(3-2x\right)\)
k, 5(2x-3)- 4(5x-7)\(\ge19-2\left(x+11\right)\)
l, \(\dfrac{2x-5}{3}-\dfrac{3x-1}{2}< \dfrac{3-x}{5}-\dfrac{2x-1}{4}\)
m, \(5x-\dfrac{3-2x}{2}>\dfrac{7x-5}{2}+x\)
n, \(\dfrac{7x-2}{3}-2x< 5-\dfrac{x-2}{4}\)
