3+5x4:2x3:9-9= \(\frac{-8}{3}\)

Sai đề nha!

sai đề rồi

c) Ta có: \(\dfrac{5x^4+9x^3-2x^2-4x-8}{x-1}\)

\(=\dfrac{5x^4-5x^3+14x^3-14x^2+12x^2-12x+8x-8}{x-1}\)

\(=\dfrac{5x^3\left(x-1\right)+14x^2\left(x-1\right)+12x\left(x-1\right)+8\left(x-1\right)}{x-1}\)

\(=5x^3+14x^2+12x+8\)

d) Ta có: \(\dfrac{5x^3+14x^2+12x+8}{x+2}\)

\(=\dfrac{5x^3+10x^2+4x^2+8x+4x+8}{x+2}\)

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

\(=5x^2+4x+4\)

c) Ta có: \(\dfrac{5x^4+9x^3-2x^2-4x-8}{x-1}\)

\(=\dfrac{5x^4-5x^3+14x^3-14x^2+12x^2-12x+8x-8}{x-1}\)

\(=\dfrac{5x^3\left(x-1\right)+14x^2\left(x-1\right)+12x\left(x-1\right)+8\left(x-1\right)}{x-1}\)

\(=5x^3+14x^2+12x+8\)

\(a\left(x\right)=5x^4-3x^2-2x^3+4-5x^4+5x^2-x+2x^3+1\)

\(=2x^2+4-x\)

Bậc : 2 

\(a\left(x\right)=5x^4-3x^2-2x^3+4-5x^4+5x^2-x+2x^3+1\)

\(a\left(x\right)=\left(5x^4-5x^4\right)+\left(2x^3-2x^3\right)+\left(5x^2-3x^2\right)-x+\left(4+1\right)\)

\(a\left(x\right)=2x^2-x+5\). Bậc của \(a\left(x\right)\) là 2

em nhầm, em xin lỗi : \(=2x^2+5-x\)

b) \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2013.2015}\)

\(=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2013.2015}\right)\)

\(=\frac{1}{2}\left(\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{2015-2013}{2013.2015}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2013}-\frac{1}{2015}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{2015}\right)=\frac{1007}{2015}\)

Phương trình tương đương với: 

\(\frac{1007X}{2015}=\frac{4}{2015}\Leftrightarrow X=\frac{4}{1007}\)

c) \(\frac{x+1}{2015}+\frac{x+2}{2016}=\frac{x+3}{2017}+\frac{x+4}{2018}\)

\(\Leftrightarrow\frac{x+1}{2015}-1+\frac{x+2}{2016}-1=\frac{x+3}{2017}-1+\frac{x+4}{2018}-1\)

\(\Leftrightarrow\frac{x-2014}{2015}+\frac{x-2014}{2016}=\frac{x-2014}{2017}+\frac{x-2014}{2018}\)

\(\Leftrightarrow x-2014=0\)

\(\Leftrightarrow x=2014\)

3, đk : x =< 3/5 

TH1 : \(x-2=3-5x\Leftrightarrow6x=5\Leftrightarrow x=\dfrac{5}{6}\)(ktm) 

TH2 : \(x-2=5x-3\Leftrightarrow4x=1\Leftrightarrow x=\dfrac{1}{4}\)(tm) 

4, \(\Leftrightarrow8x-14=3x+21\Leftrightarrow5x=35\Leftrightarrow x=7\)

Bài 3:

\(\Leftrightarrow x-2=3-5x\\ \Leftrightarrow x+5x=3+2\\ \Leftrightarrow6x=5\\ \Leftrightarrow x=\dfrac{5}{6}\)

Vậy \(x=\dfrac{5}{6}\)

Bài 4:

\(\Leftrightarrow8x-14=3x+3+18\)

\(\Leftrightarrow8x-3x=3+18+14\\ \Leftrightarrow5x=35\\ \Leftrightarrow x=\dfrac{35}{5}=7\)

Vậy x = 7

3. \(x-2=3-5x\\ \Leftrightarrow x+5x=3+2\\ \Leftrightarrow6x=5\\ \Leftrightarrow x=\dfrac{5}{6}\)

Vậy PT có tập nghiệm S = { \(\dfrac{5}{6}\)}

4. \(2\left(4x-7\right)=3\left(x+1\right)+18\\ \Leftrightarrow8x-14=3x+3+18\\ \Leftrightarrow8x-3x=3+18+14\\ \Leftrightarrow5x=35\\ \Leftrightarrow x=7\)

Vậy PT có tập nghiệm S = { 7 }

400-36= 364

a) (-x⁶ + 5x⁴ – 2x³) : (0,5x²)

= (-x⁶ : 0,5x²) + (5x⁴ : 0,5x²) + (-2x³ : 0,5x²)

= -2x⁴ + 10x² – 4x

b)

1: Sửa đề: 3x-5

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

2: \(=\dfrac{5x^4-5x^3+14x^3-14x^2+12x^2-12x+8x-8}{x-1}\)

=5x^2+14x^2+12x+8

3: \(=\dfrac{5x^3+10x^2+4x^2+8x+4x+8}{x+2}=5x^2+4x+4\)

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

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