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TH
Thầy Hùng Olm
Manager VIP
5 tháng 11 2022

x2-3x+5x-15-x2-2x 

=-15

  \(\left(x-3\right).\left(x+5\right)-x.\left(x+2\right)\)

\(=x^2+5x-3x-15-x^2-2x\)

\(=-15\)

10 tháng 11 2023

\(\left(x-2\right)\left(x-3\right)-2x\left(1-x\right)\)

\(=x^2-3x-2x+6-2x+2x^2\)

\(=x^2-5x+6-2x+2x^2\)

\(=3x^2-7x+6\) 

_______________

\(\left(x+5\right)^2-\left(x+3\right)\left(x-2\right)\)

\(=\left(x^2+10x+25\right)-\left(x^2-2x+3x-6\right)\)

\(=x^2+10x+25-x^2-x+6\)

\(=9x+31\)

AH
Akai Haruma
Giáo viên
26 tháng 11 2023

Lời giải:
ĐKXĐ: $x\neq 2; x\neq -3$

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

23 tháng 6 2021

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

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

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

3 tháng 9 2023

\(\left(x-3\right)\left(x-5\right)-\left(x-4\right)^2\)

\(=x^2-5x-3x+15-\left(x^2-8x+16\right)\)

\(=x^2-5x-3x+15-x^2+8x-16\)

\(=x^2-x^2-8x+8x+15-16=-1\)

3 tháng 9 2023

(x - 3)(x - 5) - (x - 4)²

= x² - 5x - 3x + 15 - x² + 8x - 16

= (x² - x²) + (-5x - 3x + 8x) + (15 - 16)

= -1

22 tháng 10 2023

1:

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

\(=4x^2-20x+25-4x^2-12x\)

=-32x+25

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

\(=x^3-6x^2+12x-8-\left(x^3-8\right)-6\left(x^2-16\right)\)

\(=-6x^2+12x-6x^2+96=-12x^2+12x+96\)

c: \(\left(x-1\right)^2-2\left(x-1\right)\left(x+2\right)+\left(x+2\right)^2+5\left(2x-3\right)\)

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

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

\(=9+10x-15=10x-6\)

2: 

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

\(=9x^2-12x+4-5x^2+20x+4x-4\)

\(=4x^2+12x\)

b: \(\left(3-x\right)\left(x^2+3x+9\right)+\left(x-3\right)^3\)

\(=27-x^3+x^3-9x^2+27x-27\)

\(=-9x^2+27x\)

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

\(=\left(x-4\right)\left(x+4\right)\left(x-4-x-4\right)+3\left(x^2-16\right)\)

\(=\left(x^2-16\right)\left(-8\right)+3\left(x^2-16\right)\)

\(=-5\left(x^2-16\right)=-5x^2+80\)

2 tháng 12 2021

\(\left(x-1\right)^3-x\left(x-2\right)\left(x+2\right)+3\left(x-5\right)^2\\ =x^3-3x^2+3x-1-x\left(x^2-4\right)+3\left(x^2-10x+25\right)\)

\(=x^3-3x^2+3x-1-x^3+4x+3x^2-30x+75\)

\(=74-23x\)

26 tháng 12 2021

\(=\dfrac{x-5+3x+15-2x-6}{\left(x-5\right)\left(x+5\right)}\cdot\dfrac{x+5}{2}\)

\(=\dfrac{2x+4}{x-5}\cdot\dfrac{1}{2}=\dfrac{x+2}{x-5}\)