Ta có:
\(\frac{x-2}{2x^2+3}=\frac{2x^2-4x}{Q}\)
\(\Leftrightarrow\frac{x-2}{2x^2+3}=\frac{2x\left(x-2\right)}{Q}\)
\(\Leftrightarrow Q=\frac{2x\left(x-2\right)\left(2x^2+3\right)}{x-2}\)
\(\Leftrightarrow Q=2x\left(2x^2+3\right)\)
\(\Leftrightarrow Q=4x^3+6x\)
Vậy \(Q=4x^3+6x\)
Chúc bạn học tốt@@
\(Q=2x\cdot\left(2x^2+3\right)\)
2.tìm x
a)3x(12x-4)-9x(4x-3)=30
b)4x(7x-5)-7x(4x-2)=-12
c)3(2x-3)+2(2-x)=-3
d)2x(\(x^2-2\))+x\(^2\left(1-2x\right)-x^2=-12\)
Bài 4:
a, Tìm GTLN
\(Q=-x^2-y^2+4x-4y+2\)
b, Tìm GTLN
\(A=-x^2-6x+5\)
\(B=-4x^2-9y^2-4x+6y+3\)
c, TÌm GTNN
\(P=x^2+y^2-2x+6y+12\)
Rút gọn biểu thức:
a, (3x-5).(2x+3)-(2x-3).(3x+7)-2x(x-4)
b,(x\(^2\)+2)\(^2\)-(x+2).(x-2).(x\(^2\)+4)
c,(2x-y)\(^2\)-2(x+3y)\(^2\)-(1+3x)(3x-1)
d,(x\(^2\)-1)\(^3\)-(x\(^4\)+x\(^2\)+1)(x\(^2\)-1)
e,(2x-1)\(^2\)-2(4x\(^2\)-1)+(2x+1)\(^2\)
g,(x-y+z)\(^2\)+(y-z)\(^2\)-2(x-y+z).(z-y)
h,(2x+3)\(^2\)+(2x+5)\(^2\)-(4x+6)(2x+5)
i,5x\(^2\)-(10x\(^3\)+15x\(^2\)-5x):(-5x)-3(x+1)
Bµi 5: Gi¶i PT sau.
\(a,\frac{5x-2}{2-2x}+\frac{2x-1}{2}+\frac{x^2+x-3}{1-x}=1\)
b,\(\frac{6x-1}{2-x}+\frac{9x+4}{x+2}=\frac{3x^2-2x+1}{x^2-4}\)
\(c,\frac{1}{x-1}+\frac{2x^2-5}{x^3-1}=\frac{4}{x^2+x+1}\)
d) (x2 + 4x + 8)2 + 3x(x2 + 4x + 8) + 2x2 = 0
e) x4 + 2x3 + 4x2 + 2x + 1 = 0
\(f,\frac{3x-1}{x-1}-\frac{2x+5}{x+3}+\frac{4}{x^2+2x-3}=1\)
bài 2 : thực hiện phép tính
a. \(\frac{5x+10}{4x-8}.\frac{4-2x}{x+2}\)
b. \(\frac{12x}{5y^3}.\frac{15y^4}{8x^3}\)
c.\(\frac{4y^2}{11x^4}.\left(-\frac{3x^2}{8y}\right)\)
d.\(\frac{x^{2-4}}{3x+12}.\frac{x+4}{2x-4}\)
e.\(\frac{5x+10}{4x-8}.\frac{4-2x}{x+2}\)
f.\(\frac{x^2-36}{2x+10}.\frac{3}{6-x}\)
g.\(\frac{x^2-9y^2}{x^2y^2}.\frac{3xy}{2x-6}\)
h.\(\frac{1-4x^2}{x^2+4x}:\frac{2-4x}{3x}\)
i.\(\frac{a^2+ab}{b-a}:\frac{a+b}{2a^2-2b^2}\)
j.\(\frac{x+y}{y-x}:\frac{x^2+xy}{3x^2-3y^2}\)
k.\(\frac{1-4x^2}{x^2+4x}:\frac{2-4x}{3x}\)
a,\(\dfrac{x^3+2x}{x^3+1}+\dfrac{2x}{x^2-x+1}+\dfrac{1}{x+1}\)
b,\(\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}+\dfrac{3x-2}{2x-4x^2}\)
Bài 4: Giải các phương trình sau
a) 4(x+5)(x+6)(x+10)(x+12)=\(3x^2\)
b) \(\frac{1}{x^2-3x+3}+\frac{2}{x^2-3x+4}=\frac{6}{x^2-3x+5}\)
c) \(\frac{4x}{4x^2-8x+7}+\frac{3x}{4x^2-10x+7}=1\)
d) \(\dfrac{2x}{2x^2-5x+3}+\dfrac{13x}{2x^2+x+3}=6\)
tìm x biết
a) \(x^2-2x-3=0\)
b) \(2x^2+5x-3=0\)
c) \(x^4-27x=0\)
d) \(2x\left(x-3\right)-\left(3-x\right)=0\)
e)\(x^2-9=2\left(x+3\right)^2\)
f)\(4x^2-4x+1=\left(5-x\right)^2\)
g) \(4x^2-8x+4=2\left(1-x\right)\left(1+x\right)\)
Cộng các phân tử:
a)\(\dfrac{2x-3}{x}+\dfrac{1-x}{x+2}+\dfrac{4x}{x-1}\)
b)\(\dfrac{1}{1+x}+\dfrac{1}{x-1}+\dfrac{3x}{1-x^2}\)
c)\(\dfrac{x^3}{x+1}+\dfrac{x^2}{x-1}+\dfrac{1}{x+1}+\dfrac{1}{x-1}\)
d)\(\dfrac{2x+y}{2x^2-xy}+\dfrac{16x}{y^2-4x^2}+\dfrac{2x-y}{2x^2+xy}\)
