(1+1/3)x(1+1/8)x...x(1+1/2499)
Rút gọn A
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NN
2
5 tháng 2 2022
A = \(\left(1+\frac{1}{3}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{15}\right)\)\(...\left(1+\frac{1}{2499}\right)\)
A = \(\left(\frac{3}{3}+\frac{1}{3}\right)\left(\frac{8}{8}+\frac{1}{8}\right)\left(\frac{15}{15}+\frac{1}{15}\right)\)\(...\left(\frac{2499}{2499}+\frac{1}{2499}\right)\)
A = \(\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.....\frac{2500}{2499}\)
A = \(\frac{4.9.16.....2500}{3.8.15.....2499}\)
A = \(\frac{\left(2.2\right)\left(3.3\right)\left(4.4\right)...\left(50.50\right)}{3.8.15.24.....2499}\)
A = \(\frac{2.3.4.....50}{3.4.5.6.....51}\)
A = \(\frac{2}{51}\)
Vậy A = \(\frac{2}{51}\)
( Nếu sai mong bạn thông cảm ạ ! )
_HT_
YN
5 tháng 2 2022
Answer:
\(A=\left(1+\frac{1}{3}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{15}\right)...\left(1+\frac{1}{2499}\right)\)
\(=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}...\frac{2500}{2499}\)
\(=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}...\frac{50^2}{49.51}\)
\(=\frac{2^2.3^2.4^2...50^2}{1.3.2.4.3.5...49.51}\)
\(=\frac{2.50}{51}\)
\(=\frac{100}{51}\)
14 tháng 1
\(A=\left(1+\dfrac{1}{3}\right)\cdot\left(1+\dfrac{1}{8}\right)\left(1+\dfrac{1}{15}\right)\cdot...\left(1+\dfrac{1}{2499}\right)\)
\(=\dfrac{4}{3}\cdot\dfrac{9}{8}\cdot...\cdot\dfrac{2500}{2499}\)
\(=\dfrac{2\cdot2}{1\cdot3}\cdot\dfrac{3\cdot3}{2\cdot4}\cdot...\cdot\dfrac{50\cdot50}{49\cdot51}\)
\(=\dfrac{2\cdot3\cdot4\cdot...\cdot50}{1\cdot2\cdot3\cdot...\cdot49}\cdot\dfrac{2\cdot3\cdot...\cdot50}{3\cdot4\cdot...\cdot51}\)
\(=\dfrac{50}{1}\cdot\dfrac{2}{51}=\dfrac{100}{51}\)
10 tháng 11 2021
a.\(A=\dfrac{x^2-4x+4}{x^3-2x^2-\left(4x-8\right)}=\dfrac{\left(x-2\right)^2}{x^2\left(x-2\right)-4\left(x-2\right)}=\dfrac{\left(x-2\right)^2}{\left(x^2-4\right)\left(x-2\right)}=\dfrac{x-2}{\left(x-2\right)\left(x+2\right)}=\dfrac{1}{x+2}\)
10 tháng 11 2021
\(A=\dfrac{\left(x-2\right)^2}{x^2\left(x-2\right)-4\left(x-2\right)}\left(x\ne\pm2\right)\\ A=\dfrac{\left(x-2\right)^2}{\left(x-2\right)^2\left(x+2\right)}=\dfrac{1}{x+2}\\ B=\dfrac{x+2-x+\sqrt{x}-1}{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}\cdot\dfrac{4\sqrt{x}}{3}\left(x>0\right)\\ B=\dfrac{4\sqrt{x}\left(\sqrt{x}+1\right)}{3\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}=\dfrac{4\sqrt{x}}{3\left(x-\sqrt{x}+1\right)}\)
NT
0
1 tháng 8 2021
A = \(\left(3x-1\right)^2+2\left(3x-1\right)\left(2x+1\right)+\left(2x+1\right)^2\)
A = \(\left(3x-1+2x+1\right)^2\)
HN
1 tháng 8 2021
A)
<=>(3x)^2−2×3x+1+2(3x−1)(2x+1)+(2x+1)^2
<=>(3x)^2−2×3x+1+(6x−2)(2x+1)+(2x+1)^2
<=>(3x)^2−2×3x+1+12x^2+6x−4x−2+(2x+1)^2
<=>(3x)^2−2×3x+1+12x^2+6x−4x−2+(2x)^2+2×2x+1
<=>32x^2−2×3x+1+12x^2+6x−4x−2+(2x)^2+2×2x+1
<=>9x^2−2×3x+1+12x^2+6x−4x−2+(2x)^2+2×2x+1
<=>9x^2−2×3x+1+12x^2+6x−4x−2+2^2x^2+2×2x+1
<=>9x^2−2×3x+1+12x^2+6x−4x−2+4x^2+2×2x+1
<=>9x^2−6x+1+12x^2+6x−4x−2+4x^2+2×2x+1
<=>9x^2−6x+1+12x^2+6x−4x−2+4x^2+4x+1
<=>(9x^2+12x^2+4x^2)+(−6x+6x−4x+4x)+(1−2+1)
<=> 25x^2
B)
<=>2x(4x^2−6x+9)+3(4x^2−6x+9)+8(1−x)(1+x+x^2)
<=>8x^3−12x^2+18x+3(4x^2−6x+9)+8(1−x)(1+x+x^2)
<=>8x^3−12x^2+18x+12x^2−18x+27+8(1−x)(1+x+x^2)
<=>8x^3−12x^2+18x+12x^2−18x+27+(8−8x)(1+x+x^2)
<=>8x^3−12x^2+18x+12x^2−18x+27+8(1+x+x^2)−8x(1+x+x^2)
<=>8x^3−12x^2+18x+12x^2−18x+27+8+8x+8x^2−8x(1+x+x^2)
<=>8x^3−12x^2+18x+12x^2−18x+27+8+8x+8x^2−(8x+8x2+8x^3)
<=>8x^3−12x^2+18x+12x^2−18x+27+8+8x+8x^2−8x−8x^2−8x^3
<=>(8x^3−8x^3)+(−12x^2+12x^2+8x^2−8x^2)+(18x−18x+8x−8x)+(27+8)
<=> 35
TT
0
H9
HT.Phong (9A5)
CTVHS
4 tháng 9 2023
\(A=\left(\dfrac{\sqrt{x}-1}{3\sqrt{x}-1}-\dfrac{1}{3\sqrt{x}+1}+\dfrac{8\sqrt{x}}{9x-1}\right):\left(1-\dfrac{3\sqrt{x}-2}{3\sqrt{x}+1}\right)\) (ĐK: \(x\ge0;x\ne\dfrac{1}{9}\))
\(A=\left[\dfrac{\sqrt{x}-1}{3\sqrt{x}-1}-\dfrac{1}{3\sqrt{x}+1}+\dfrac{8\sqrt{x}}{\left(3\sqrt{x}\right)^2-1^2}\right]:\left[\dfrac{\left(3\sqrt{x}+1\right)\cdot1}{3\sqrt{x}+1}-\dfrac{3\sqrt{x}-2}{3\sqrt{x}+1}\right]\)
\(A=\left[\dfrac{\sqrt{x}-1}{3\sqrt{x}-1}-\dfrac{1}{3\sqrt{x}+1}+\dfrac{8\sqrt{x}}{\left(3\sqrt{x}+1\right)\left(3\sqrt{x}-1\right)}\right]:\dfrac{3\sqrt{x}+1-3\sqrt{x}+2}{3\sqrt{x}+1}\)
\(A=\left[\dfrac{\left(\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)}{\left(3\sqrt{x}+1\right)\left(3\sqrt{x}-1\right)}-\dfrac{3\sqrt{x}-1}{\left(3\sqrt{x}+1\right)\left(3\sqrt{x}-1\right)}+\dfrac{8\sqrt{x}}{\left(3\sqrt{x}+1\right)\left(3\sqrt{x}-1\right)}\right]:\dfrac{3}{3\sqrt{x}+1}\)
\(A=\dfrac{3x+\sqrt{x}-3\sqrt{x}-1-3\sqrt{x}+1+8\sqrt{x}}{\left(3\sqrt{x}+1\right)\left(3\sqrt{x}-1\right)}\cdot\dfrac{3\sqrt{x}+1}{3}\)
\(A=\dfrac{3x+3\sqrt{x}}{\left(3\sqrt{x}+1\right)\left(3\sqrt{x}-1\right)}\cdot\dfrac{3\sqrt{x}+1}{3}\)
\(A=\dfrac{3\sqrt{x}\left(\sqrt{x}+1\right)}{\left(3\sqrt{x}+1\right)\left(3\sqrt{x}-1\right)}\cdot\dfrac{3\sqrt{x}+1}{3}\)
\(A=\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{3\sqrt{x}-1}\)
\(A=\dfrac{x+\sqrt{x}}{3\sqrt{x}-1}\)
4 tháng 9 2023
\(A=\left(\dfrac{\sqrt{x}-1}{3\sqrt{x}-1}-\dfrac{1}{3\sqrt{x}+1}+\dfrac{8\sqrt{x}}{\left(3\sqrt{x}+1\right)\left(3\sqrt{x}-1\right)}\right):\dfrac{3\sqrt{x}+1-3\sqrt{x}+2}{3\sqrt{x}+1}\)
\(=\dfrac{\left(\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)-3\sqrt{x}+1+8\sqrt{x}}{\left(3\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)}\cdot\dfrac{3\sqrt{x}+1}{3}\)
\(=\dfrac{3x+\sqrt{x}-3\sqrt{x}-1+5\sqrt{x}+1}{3\sqrt{x}-1}\cdot\dfrac{1}{3}\)
\(=\dfrac{3x+3\sqrt{x}}{3\sqrt{x}-1}\cdot\dfrac{1}{3}\)
\(=\dfrac{x+\sqrt{x}}{3\sqrt{x}-1}\)
H
1
4 tháng 1 2022
2: ĐKXĐ: \(x\ne2\)
\(\dfrac{3x^2+6x+12}{x^3-8}=\dfrac{3\left(x^2+2x+4\right)}{\left(x-2\right)\left(x^2+2x+4\right)}=\dfrac{3}{x-2}\)
giúp mình nhanh nhé mình đang cần gấp.