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MA
1
9 tháng 12 2021
\(P=\dfrac{x^3+8y^3}{4^3+4^3}=\dfrac{\left(x+2y\right)^3-3\cdot x\cdot2y\cdot\left(x+2y\right)}{128}\)
\(=\dfrac{\left(-8\right)^3-6\cdot\left(-6\right)\cdot\left(-8\right)}{128}=\dfrac{128-6\cdot48}{128}=-\dfrac{5}{4}\)
23 tháng 12 2021
a: \(M=\dfrac{5x+5-8-4x+4}{\left(x-1\right)\left(x+1\right)}=\dfrac{x+1}{\left(x-1\right)\left(x+1\right)}=\dfrac{1}{x-1}\)
b: \(N=\dfrac{5x+5-8-4x+4}{\left(x-1\right)\left(x+1\right)}=\dfrac{x+1}{\left(x-1\right)\left(x+1\right)}=\dfrac{1}{x-1}\)
23 tháng 12 2021
1. \(M=\dfrac{5}{x-1}-\dfrac{8}{x^2-1}-\dfrac{4}{x+1}\left(x\ne\pm1\right).\)
\(M=\dfrac{5\left(x+1\right)-8-4\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}\)\(M=\dfrac{5x+5-8-4x+4}{\left(x-1\right)\left(x+1\right)}=\dfrac{x+1}{\left(x-1\right)\left(x+1\right)}\)
\(M=\dfrac{1}{x-1}.\)
2. \(N=\dfrac{5}{x-1}+\dfrac{8}{1-x^2}-\dfrac{4}{x+1}\left(x\ne\pm1\right).\)
\(N=\dfrac{5\left(x+1\right)-8-4\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{5x+5-8-4x+4}{\left(x-1\right)\left(x+1\right)}\)
\(N=\dfrac{x+1}{\left(x-1\right)\left(x+1\right)}=\dfrac{1}{x-1}.\)
3. \(Q=\dfrac{1}{2x-1}-\dfrac{4}{4x^2-1}-\dfrac{2}{2x+1}\left(x\ne\pm\dfrac{1}{2}\right).\)
\(Q=\dfrac{2x+1-4-2\left(2x-1\right)}{\left(2x-1\right)\left(2x+1\right)}=\dfrac{2x-3-4x+2}{\left(2x-1\right)\left(2x+1\right)}\)
\(Q=\dfrac{-2x-1}{\left(2x-1\right)\left(2x+1\right)}=\dfrac{-1}{2x-1}.\)
4. \(F=\dfrac{x+3}{x-2}+\dfrac{x+2}{3-x}+\dfrac{x+2}{x^2-5x+6}\left(x\ne2,x\ne3\right).\)
\(F=\dfrac{x+3}{x-2}-\dfrac{x+2}{x-3}+\dfrac{x+2}{\left(x-3\right)\left(x-2\right)}\)
\(F=\dfrac{\left(x+3\right)\left(x-3\right)-\left(x+2\right)\left(x-2\right)+x+2}{\left(x-2\right)\left(x-3\right)}\)
\(F=\dfrac{x^2-9-x^2+4+x+2}{\left(x-2\right)\left(x-3\right)}=\dfrac{x-3}{\left(x-2\right)\left(x-3\right)}\)
\(F=\dfrac{1}{x-2}.\)
10 tháng 9 2021
a: Ta có: \(8x\left(x-2017\right)-2x+4034=0\)
\(\Leftrightarrow\left(x-2017\right)\left(4x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2017\\x=\dfrac{1}{4}\end{matrix}\right.\)
11 tháng 9 2021
c: Ta có: \(4-x=2\left(x-4\right)^2\)
\(\Leftrightarrow2\left(x-4\right)^2+x-4=0\)
\(\Leftrightarrow\left(x-4\right)\left(2x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=\dfrac{7}{2}\end{matrix}\right.\)
15 tháng 11 2021
\(a,=x^2+x+4x+4=\left(x+1\right)\left(x+4\right)\\ b,=x^2+2x-3x-6=\left(x-3\right)\left(x+2\right)\\ c,=x^2-2x-3x+6=\left(x-2\right)\left(x-3\right)\\ d,=3\left(x^2-2x+5x-10\right)=3\left(x-2\right)\left(x+5\right)\\ e,=-3x^2+6x-x+2=\left(x-2\right)\left(1-3x\right)\\ f,=x^2-x-6x+6=\left(x-1\right)\left(x-6\right)\\ h,=4\left(x^2-3x-6x+18\right)=4\left(x-3\right)\left(x-6\right)\\ i,=3\left(3x^2-3x-8x+5\right)=3\left(x-1\right)\left(3x-8\right)\\ k,=-\left(2x^2+x+4x+2\right)=-\left(2x+1\right)\left(x+2\right)\\ l,=x^2-2xy-5xy+10y^2=\left(x-2y\right)\left(x-5y\right)\\ m,=x^2-xy-2xy+2y^2=\left(x-y\right)\left(x-2y\right)\\ n,=x^2+xy-3xy-3y^2=\left(x+y\right)\left(x-3y\right)\)
8 tháng 5 2021
ĐKXĐ: \(x\notin\left\{0;-9\right\}\)
Ta có: \(\dfrac{1}{x+9}-\dfrac{1}{x}=\dfrac{1}{5}+\dfrac{1}{4}\)
\(\Leftrightarrow\dfrac{20x}{20x\left(x+9\right)}-\dfrac{20\left(x+9\right)}{20x\left(x+9\right)}=\dfrac{4x\left(x+9\right)+5x\left(x+9\right)}{20x\left(x+9\right)}\)
Suy ra: \(4x^2+36x+5x^2+45x=20x-20x-180\)
\(\Leftrightarrow9x^2+81x+180=0\)
\(\Leftrightarrow x^2+9x+20=0\)
\(\Leftrightarrow x^2+4x+5x+20=0\)
\(\Leftrightarrow x\left(x+4\right)+5\left(x+4\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\left(nhận\right)\\x=-5\left(nhận\right)\end{matrix}\right.\)
Vậy: S={-4;-5}
KK
13 tháng 9 2021
a. (3x - 1)2 - 16
= (3x - 1)2 - 42
= (3x - 1 - 4)(3x - 1 + 4)
= (3x - 5)(3x + 3)
= 3(3x - 5)(x + 1)
b. (5x - 4)2 - 49x2
= (5x - 4)2 - (7x)2
= (5x - 4 - 7x)(5x - 4 + 7x)
= \(\left(-2x-4\right)\left(2x-4\right)\)
= 2(-x - 2) . 2(x - 2)
= 4(-x - 2)(x - 2)
c. (2x + 5)2 - (x - 9)2
= (2x + 5 - x + 9)(2x + 5 + x - 9)
= (x + 14)(3x - 4)
F
13 tháng 9 2021
2.
a)(3x-1)2-16 = (3x-1)2-42
=(3x-1-4).(3x-1+4)= (3x-5).(3x+3)
b)(5x-4)2-49x2 =(5x-4)2-(7x)2
= (5x-4-7x).(5x-4+7x) = (-2x-4).(12x-4)
c)(2x+5)2-(x-9)2 =(2x+5-x+9).(2x+5+x-9) =(x+14).(3x-4)
d)(3x+1)2-4.(x-2)2 =(3x+1)2-[2.(x-2)]2 = [3x+1-2.(x-2)].[3x+1+2.(x-2)]
= (3x+1-2x+4).(3x+1+2x-4)
= (x+5).(5x-3)
e)9.(2x+3)2-4.(x+1)2 =[3.(2x+3)]2-[2.(x+1)]2
=[3.(2x+3)-2.(x+1)].[3.(2x+3)+2.(x+1)]
=(6x+9-2x-2).(6x+9+2x+2)
=(4x+7).(8x+11)
a)\(4x^2+x=x\left(4x+1\right)\)
b)\(3x-9y=3\left(x-3y\right)\)
c)\(5\left(x-y\right)-x\left(x-y\right)=\left(5-x\right)\left(x-y\right)\)
d)\(4\left(2x-y\right)-x\left(y-2x\right)=-4\left(y-2x\right)-x\left(y-2x\right)=\left(-4-x\right)\left(y-2x\right)\)
e)\(\left(2x+1\right)^2+2\left(2x+1\right)=\left(2x+1\right)\left(2x+1+2\right)=\left(2x+1\right)\left(2x+3\right)\)
f)\(y\left(x+y\right)-y-x=y\left(x+y\right)-\left(x+y\right)=\left(y-1\right)\left(x+y\right)\)
g)\(2y\left(x-y\right)^2+x\left(y-x\right)^2=2y\left(y-x\right)^2+x\left(y-x\right)^2=\left(2y+x\right)\left(y-x\right)^2\)
h)
h)(x-2)-(x-2)^2=(x-2)(1-x-2)=(x-2)(x-1)
i)x(x-3)-2x+6=x(x-3)-2(x-3)=(x-3)(x-2)