\(\dfrac{x}{x^2-5x}+\dfrac{x+1}{4x+20}=\dfrac{x}{x\left(x-5\right)}+\dfrac{x+1}{4\left(x+5\right)}\)

\(=\dfrac{x\cdot4\left(x+5\right)}{4x\left(x-5\right)\left(x+5\right)}+\dfrac{\left(x+1\right)\cdot x\left(x-5\right)}{4\cdot x\left(x-5\right)\left(x+5\right)}\)

\(=\dfrac{4x\left(x+5\right)}{4x\left(x-5\right)\left(x+5\right)}+\dfrac{\left(x+1\right)\left(x^2-5x\right)}{4x\left(x-5\right)\left(x+5\right)}\)

\(=\dfrac{4x\left(x+5\right)+\left(x+1\right)\left(x^2-5x\right)}{4x\left(x+5\right)\left(x-5\right)}\)

\(=\dfrac{4x^2+20x+x^3-5x^2+x^2-5x}{4x\left(x+5\right)\left(x-5\right)}\)

\(=\dfrac{x^3+15x}{4x\left(x+5\right)\left(x-5\right)}=\dfrac{x\left(x^2+15\right)}{4x\left(x+5\right)\left(x-5\right)}=\dfrac{x^2+15}{4\left(x+5\right)\left(x-5\right)}=\dfrac{x^2+15}{4\left(x^2-25\right)}=\dfrac{x^2+15}{4x^2-100}\)

\(\dfrac{3-3x}{\left(1+x\right)^2}:\dfrac{6x^2-6}{x+1}\)

\(=\dfrac{3\left(1-x\right)}{\left(x+1\right)^2}:\dfrac{6\left(x^2-1\right)}{x+1}\)

\(=\dfrac{-3\left(x-1\right)}{\left(x+1\right)^2}:\dfrac{6\left(x+1\right)\left(x-1\right)}{x+1}\)

\(=\dfrac{-3\left(x-1\right)}{\left(x+1\right)^2}\cdot\dfrac{x+1}{6\left(x+1\right)\left(x-1\right)}\)

\(=\dfrac{-3\left(x-1\right)\left(x+1\right)}{6\left(x+1\right)^3\left(x-1\right)}=\dfrac{-3\left(x+1\right)}{6\left(x+1\right)\left(x+1\right)^2}=\dfrac{-3}{6\left(x+1\right)^2}=\dfrac{-1}{2\left(x+1\right)^2}\)

b) Bạn có thể viết kiểu latex được không ạ ?

a) \(MTC=a^2x^2b^2\)

\(NTP:a^2x^2b^2:a^2x=xb^2\)

\(a^2x^2b^2:x^2b=a^2b\)

\(a^2x^2b^2:b^2a=ax^2\)

Quy đồng :

\(\dfrac{a+x}{a^2x}=\dfrac{\left(a+x\right)\cdot xb^2}{a^2x.xb^2}=\dfrac{axb^2+x^2b^2}{a^2x^2b^2}\)

\(\dfrac{a+b}{x^2b}=\dfrac{\left(a+b\right)\cdot a^2b}{x^2b\cdot a^2b}=\dfrac{a^3b+a^2b^2}{a^2x^2b^2}\)

\(\dfrac{b+a}{b^2a}=\dfrac{\left(b+a\right)\cdot ax^2}{b^2a\cdot ax^2}=\dfrac{abx^2+a^2x^2}{a^2x^2b^2}\)

a) \(\left(x^5+4x^3-6x^2\right):4x^2\)

\(=\left(x^5:4x^2\right)+\left(4x^3:4x^2\right)+\left(-6x^2:4x^2\right)\)

\(=\dfrac{1}{4}x^3+x-\dfrac{3}{2}\)

b) 

Vậy \(\left(x^3+x^2-12\right):\left(x-2\right)=x^2+3x+6\)

c) (-2x⁵ : 2x²) + (3x² : 2x²) + (-4x^3 : 2x^2)

= \(-x^3+\dfrac{3}{2}-2x\)

d) \(\left(x^3-64\right):\left(x^2+4x+16\right)\)

\(=\left(x-4\right)\left(x^2+4x+16\right):\left(x^2+4x+16\right)\)

\(=x-4\)

(dùng hẳng đẳng thức thứ 7)

Bài 2 :

a) 3x(x - 2) - 5x(1 - x) - 8(x² - 3)

= 3x² - 6x - 5x + 5x² - 8x² + 24

= (3x² + 5x² - 8x²) + (-6x - 5x) + 24 

= -11x + 24

b) (x - y)(x² + xy + y²) + 2y³

= x³ - y³ + 2y³

= x³ + y³ 

c) (x - y)² + (x + y)² - 2(x - y)(x + y)

= (x - y)² - 2(x - y)(x + y) + (x + y)²

= [(x - y) + x + y)² = [x - y + x + y] = (2x)² = 4x²

1 + 1 = 2

ai tk mình 

mình tk lại cho

cam on 

1 km ô tô tiêu số lit xăng:

  12:100=0,12 (lít)

75 km ô tô tiêu số lit xăng:

 0,12.75=9 (lít)