a: ĐKXD: x<>0

\(\dfrac{14x^3+12x^2-14x}{2x}=\left(x+2\right)\left(3x-4\right)\)

=>\(\dfrac{2x\left(7x^2+6x-7\right)}{2x}=\left(x+2\right)\left(3x-4\right)\)

=>\(7x^2+6x-7=3x^2-4x+6x-8\)

=>\(7x^2+6x-7=3x^2+2x-8\)

=>\(4x^2+4x+1=0\)

=>\(\left(2x+1\right)^2=0\)

=>2x+1=0

=>x=-1/2(nhận)

b: \(\left(4x-5\right)\left(6x+1\right)-\left(8x+3\right)\left(3x-4\right)=15\)

=>\(24x^2+4x-30x-5-\left(24x^2-32x+9x-12\right)=15\)

=>\(24x^2-26x-5-24x^2+23x+12=15\)

=>-3x+7=15

=>-3x=8

=>\(x=-\dfrac{8}{3}\)

a: =x^4-3x^5+4x^8

b: =2x^3+2x^2+4x

c: =4x^2+8x-5

d: =2x+3x^2+7x^4

b: =x^2+4x-5x-20

=x^2-x-20

c: =-7x^2+4x-2

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

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

Bài 1.

a)

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

b)

\(x(x+3y+1)-2y(x-1)-(y+x+1)x\\=x^2+3xy+x-2xy+2y-xy-x^2-x\\=(x^2-x^2)+(3xy-2xy-xy)+(x-x)+2y\\=2y\)

Bài 2.

a)

\((14x^3+12x^2-14x):2x=(x+2)(3x-4)\\\Leftrightarrow 14x^3:2x+12x^2:2x-14x:2x=3x^2-4x+6x-8\\ \Leftrightarrow 7x^2+6x-7=3x^2+2x-8\\\Leftrightarrow (7x^2-3x^2)+(6x-2x)+(-7+8)=0\\\Leftrightarrow 4x^2+4x+1=0\\\Leftrightarrow (2x)^2+2\cdot 2x\cdot 1+1^2=0\\\Leftrightarrow (2x+1)^2=0\\\Leftrightarrow 2x+1=0\\\Leftrightarrow 2x=-1\\\Leftrightarrow x=\frac{-1}2\)

b)

\((4x-5)(6x+1)-(8x+3)(3x-4)=15\\\Leftrightarrow 24x^2+4x-30x-5-(24x^2-32x+9x-12)=15\\\Leftrightarrow 24x^2-26x-5-(24x^2-23x-12)=15\\\Leftrightarrow 24x^2-26x-5-24x^2+23x+12=15\\\Leftrightarrow -3x+7=15\\\Leftrightarrow -3x=8\\\Leftrightarrow x=\frac{-8}3\\Toru\)

Chắc bạn ghi nhầm đề, đây là giới hạn bình thường, cứ thay số thôi:

\(=\frac{2+8+7-4-4}{2+14+20+8}=\frac{9}{44}\)

a) ( 5 - 2x )( 2x + 7 ) - 4x² + 25 = 0

<=> ( 5 - 2x )( 2x + 7 ) + ( 5 - 2x )( 5 + 2x ) = 0

<=> ( 5 - 2x )( 2x + 7 + 5 + 2x ) = 0

<=> ( 5 - 2x )( 4x + 12 ) = 0

<=> \(\orbr{\begin{cases}5-2x=0\\4x+12=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{5}{2}\\x=-3\end{cases}}\)

b) ( 5x² + 3x - 2 )² - ( 4x² - x - 5 )² = 0 ( như này chứ nhỉ ? )

<=> [ ( 5x² + 3x - 2 ) - ( 4x² - x - 5 ) ][ ( 5x² + 3x - 2 ) + ( 4x² - x - 5 ) ] = 0

<=> ( 5x² + 3x - 2 - 4x² + x + 5 )( 5x² + 3x - 2 + 4x² - x - 5 ) = 0

<=> ( x² + 4x + 3 )( 9x² + 2x - 7 ) = 0

<=> ( x² + x + 3x + 3 )( 9x² + 9x - 7x - 7 ) = 0

<=> [ x( x + 1 ) + 3( x + 1 ) ][ 9x( x + 1 ) - 7( x + 1 ) ] = 0

<=> ( x + 1 )( x + 3 )( x + 1 )( 9x - 7 ) = 0

<=> ( x + 1 )²( x + 3 )( 9x - 7 ) = 0

<=> x + 1 = 0 hoặc x + 3 = 0 hoặc 9x - 7 = 0

<=> x = -1 hoặc x = -3 hoặc x = 7/9

c) 15x⁴ - 8x³ - 14x² - 8x + 15 = 0

<=> 15x⁴ + 22x³ - 30x³ + 15x² + 15x² - 44x² - 30x + 22x + 15 = 0

<=> ( 15x⁴ + 22x³ + 15x² ) - ( 30x³ + 44x² + 30x ) + ( 15x² + 22x + 15 ) = 0

<=> x²( 15x² + 22x + 15 ) - 2x( 15x² + 22x + 15 ) + ( 15x² + 22x + 15 ) = 0

<=> ( 15x² + 22x + 15 )( x² - 2x + 1 ) = 0

<=> ( 15x² + 22x + 15 )( x - 1 )² = 0

<=> \(\orbr{\begin{cases}15x^2+22x+15=0\\\left(x-1\right)^2=0\end{cases}}\)

+) ( x - 1 )² = 0 <=> x = 1

+) 15x² + 22x + 15 = 15( x² + 22/15x + 121/225 ) + 104/15 = 15( x + 11/25 )² + 104/15 ≥ 104/15 > 0 ∀ x

Vậy phương trình có nghiệm duy nhất là x = 1

Cảm ơn bạn câu b thiếu cái mũ 2 sorry :))

\(a)\left(2x+5\right)\left(2x-7\right)-\left(-4x-3\right)^2=16\\ \Leftrightarrow4x^2-14x+10x-35-\left(16x^2+24x-9\right)=16\\ \Leftrightarrow-12x^2-28x-44=16\\ \Leftrightarrow-12x^2-28x-60=0\\ \Leftrightarrow3x^2+7x+15=0\\ \Delta=b^2-4ac=7^2-4.3.15=-131< 0\)

Vậy phương trình vô nghiệm

\( b)(8x^2 + 3)(8x^2 - 3) - (8x^2 - 1)^2 = 22\)

\(\Leftrightarrow64x^4-9-\left(64x^4-16x^2+1\right)=22\\ \Leftrightarrow-10+16x^2=22\\ \Leftrightarrow16x^2=32\\ \Leftrightarrow x^2=2\\ \Leftrightarrow x=\pm\sqrt{2}\)

Vậy \(x=\sqrt{2},x=-\sqrt{2}\)

\(c)49x^2+14x+1=0\\ \Leftrightarrow\left(7x+1\right)^2=0\\ \Leftrightarrow7x+1=0\\ \Leftrightarrow7x=-1\)

\(\Leftrightarrow\)\(x=-\dfrac{1}{7}\)

Vậy \(x=-\dfrac{1}{7}\)

\(\Leftrightarrow\)\(x=-\dfrac{1}{7}\)

a: \(=\dfrac{6x^2+9x+8x+12}{2x+3}=\dfrac{3x\left(2x+3\right)+4\left(2x+3\right)}{2x+3}\)

=3x+4

b: \(=\dfrac{5x^2-2x+15x-6}{5x-2}\)

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

c: \(=\dfrac{-8x^2+20x+2x-5-10}{2x-5}=-4x+1+\dfrac{-10}{2x-5}\)

d: \(=\dfrac{14x^2-35x+2x-5}{2x-5}=\dfrac{7x\left(2x-5\right)+\left(2x-5\right)}{2x-5}\)

=7x+1

e: \(=\dfrac{2x^3+x^2+6x^2+3x+12x+6}{2x+1}\)

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

f: \(=\dfrac{x^3-2x^2+6x^2-12x+x-2}{x-2}=x^2+6x+1\)

g: \(=\dfrac{12x^3+6x^2-4x^2-2x+6x+3}{2x+1}=6x^2-2x+3\)