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\(a,\dfrac{2x+2y}{a^2+2ab+b^2}.\dfrac{ax-ay+bx-by}{2x^2-2y^2}\)
\(=\dfrac{2\left(x+y\right)}{\left(a+b\right)^2}.\dfrac{a\left(x-y\right)+b\left(x-y\right)}{2\left(x^2-y^2\right)}\)
\(=\dfrac{2\left(x+y\right)}{\left(a+b\right)^2}.\dfrac{\left(x-y\right)\left(a+b\right)}{2\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{1}{a+b}\)
\(b,\dfrac{a+b-c}{a^2+2ab+b^2-c^2}.\dfrac{a^2+2ab+b^2+ac+bc}{a^2-b^2}\)
\(=\dfrac{a+b-c}{\left(a+b\right)^2-c^2}.\dfrac{\left(a+b\right)^2+c\left(a+b\right)}{\left(a-b\right)\left(a+b\right)}\)
\(=\dfrac{a+b-c}{\left(a+b-c\right)\left(a+b+c\right)}.\dfrac{\left(a+b\right)\left(a+b+c\right)}{\left(a-b\right)\left(a+b\right)}\)
\(=\dfrac{1}{a-b}\)
\(c,\dfrac{x^3+1}{x^2+2x+1}.\dfrac{x^2-1}{2x^2-2x+2}\)
\(=\dfrac{\left(x+1\right)\left(x^2-x+1\right)}{\left(x+1\right)^2}.\dfrac{\left(x-1\right)\left(x+1\right)}{2\left(x^2-x+1\right)}\) \(=\dfrac{x-1}{2}\) \(d,\dfrac{x^8-1}{x+1}.\dfrac{1}{\left(x^2+1\right)\left(x^4+1\right)}\) \(=\dfrac{\left(x^4\right)^2-1}{x+1}.\dfrac{1}{\left(x^2+1\right)\left(x^4+1\right)}\) \(=\dfrac{\left(x^4-1\right)\left(x^4+1\right)}{x+1}.\dfrac{1}{\left(x^2+1\right)\left(x^4+1\right)}\) \(=\dfrac{\left(x^2+1\right)\left(x^2-1\right)}{x+1}.\dfrac{1}{x^2+1}\) \(=\dfrac{\left(x-1\right)\left(x+1\right)}{x+1}\) \(=x-1\) \(e,\dfrac{x-y}{xy+y^2}-\dfrac{3x+y}{x^2-xy}.\dfrac{y-x}{x+y}\) \(=\dfrac{x-y}{y\left(x+y\right)}-\dfrac{3x+y}{x\left(x-y\right)}.\dfrac{-\left(x-y\right)}{x+y}\) \(=\dfrac{x-y}{y\left(x+y\right)}-\dfrac{3x+y}{x}.\dfrac{-1}{x+y}\) \(=\dfrac{x-y}{y\left(x+y\right)}-\dfrac{-3x-y}{x\left(x+y\right)}\) \(=\dfrac{x\left(x-y\right)+y\left(3x+y\right)}{xy\left(x+y\right)}\) \(=\dfrac{x^2-xy+3xy+y^2}{xy\left(x+y\right)}\) \(=\dfrac{x^2+2xy+y^2}{xy\left(x+y\right)}\) \(=\dfrac{\left(x+y\right)^2}{xy\left(x+y\right)}=\dfrac{x+y}{xy}\)tìm giá trị của m để pt 2x-m=1-x nhận giá trị x=-2 là nghiệm
giải hộ e với :)
\(4x^2-1=\left(2x-1\right)\left(2x+1\right)\)
\(x\left(x+y\right)-6x-6y=\left(x+y\right)\left(x-6\right)\)
\(x^2-2xy+y^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)
\(9x^2-\dfrac{1}{4}=\left(3x-\dfrac{1}{2}\right)\left(3x+\dfrac{1}{2}\right)\)
a,x2-y2-2x+2y
= (x+y)(x-y) - 2(x-y)
= (x-y)(x+y-2)
b,2x+2y-x2-xy
= 2(x+y) - x(x+y)
= (x+y)(2-x)
c,3a2-6ab+3b2-12c2
= 3(a2 - 2ab + b2 - 4c2)
= 3[(a-b)2 - 4c2)
= 3(a-b-2c)(a-b+2c)
d,x2-25+y2+2xy
= (x+y)2 - 25
= (x+y+5)(x+y-5)
e) a2+2ab+b2-ac-bc
= (a+b)2-c(a+b)
= (a+b)( a+b-c)
f) x2-2x-4x2-4y
= -3x2-2x-4y
= -(3x2+2x+4y)
g)x2y-x3-9y+9x
= x2(y-x)-9(y-x)
= (y-x)(x2-9)
h) x2(x-1)+16(1-x)
= x2(x-1)-16(x-1)
= (x-1)(x2-16)
= (x-1)(x-4)(x+4)
n) 81x2-6yz-9y2-z2
= (9x)2-[(3y)2+6yz+z2]
=(9x)2-(3y+z)2
=(9x+3y+z)(9x-3y-z)
m) xz- yz-x2+2xy-y2
= z(x-y)-(x2-2xy+y2)
= z(x-y)-(x-y)2
= (x-y)(z-x+y)
p) x2 + 8x + 15
= x2 + 3x + 5x + 15
= x(x+3) + 5(x+3)
= (x+3)(x+5)
k) x2 - x - 12
= x2 + 3x - 4x - 12
= x(x+3) - 4(x+3)
= (x+3)(x-4)