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9 tháng 12 2019

\(=\frac{x\left(16x^2-25\right)}{\left(x-3\right)\left(3-8+4x\right)}\)

\(=\frac{x\left(4x-5\right)\left(4x+5\right)}{\left(x-3\right)\left(4x-5\right)}\)

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

29 tháng 6 2017

\(=\frac{5x\left(16x^2-25\right)}{\left(x-3\right)\left(3-8+4x\right)}\)

\(=\frac{5x\left(4x-5\right)\left(4x+5\right)}{\left(x-3\right)\left(4x-5\right)}\)

\(=\frac{5x\left(4x+5\right)}{x-3}\)

\(=\frac{20x^2+25x}{x-3}\)

8 tháng 8 2017

phân tích thành nhân tử ở mẫu và tử sau đó ta rút gọn vậy là ra đáp số

8 tháng 8 2017

a) \(=\frac{5x\left(16x^2-25\right)}{\left(x-3\right)\left(4x-5\right)}\)\(\)

\(=\frac{5x\cdot\left(4x-5\right)\left(4x+5\right)}{\left(x-3\right)\left(4x-5\right)}\)

\(=\frac{5x\left(4x+5\right)}{x-3}\)

b) \(=\frac{3^2-\left(x+5\right)^2}{\left(x+2\right)^2}\)

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

\(=\frac{\left(x+2\right)\left(8+x\right)}{\left(x+2\right)^2}\)

\(=\frac{8+x}{x+2}\)

2 tháng 12 2019

a) \(\frac{x^2-16}{4x-x^2}=\frac{\left(x+4\right)\left(x-4\right)}{x\left(4-x\right)}\)

\(=\frac{\left(x+4\right)\left(x-4\right)}{-x\left(x-4\right)}=\frac{x+4}{-x}\)

b) \(\frac{x^2+4x+3}{2x+6}=\frac{x^2+3x+x+3}{2\left(x+3\right)}\)

\(=\frac{x\left(x+3\right)+\left(x+3\right)}{2\left(x+3\right)}\)

\(=\frac{\left(x+1\right)\left(x+3\right)}{2\left(x+3\right)}=\frac{x+1}{2}\)

c) \(\frac{\left(2x^2+2x\right)\left(x-2\right)^2}{\left(x^3-4x\right)\left(x+1\right)}\)

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

\(=\frac{2x\left(x-2\right)^2}{x\left(x+2\right)\left(x-2\right)}\)

\(=\frac{2x\left(x-2\right)}{x\left(x+2\right)}\)

\(=\frac{2x^2-4x}{x^2+2x}\)

d) \(\frac{x^3-x^2y+xy^2}{x^3+y^3}\)

\(=\frac{x\left(x^2-xy+y^2\right)}{\left(x+y\right)\left(x^2-xy+y^2\right)}=\frac{x}{x+y}\)

13 tháng 11 2023

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

\(=2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)\)

\(=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x\)

\(=x^3-16x^2+25x\)

16 tháng 12 2020

\(\frac{1}{x\left(x-1\right)}+\frac{1}{\left(x-1\right)\left(x-2\right)}+\frac{1}{\left(x-2\right)\left(x-3\right)}+...+\frac{1}{\left(x-4\right)\left(x-5\right)}\)

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

\(=\frac{1}{x}-\frac{1}{x-5}=\frac{x-5}{x\left(x-5\right)}-\frac{x}{x\left(x-5\right)}=\frac{-5}{x\left(x-5\right)}\)

16 tháng 12 2020

\(\frac{1}{x\left(x-1\right)}+\frac{1}{\left(x-1\right)\left(x-2\right)}+\frac{1}{\left(x-2\right)\left(x-3\right)}+...+\frac{1}{\left(x-4\right)\left(x-5\right)}\)

\(=\frac{1}{x}-\frac{1}{x-1}+\frac{1}{x-1}-\frac{1}{x-2}+...+\frac{1}{x-4}-\frac{1}{x-5}\)

\(=\frac{1}{x}-\frac{1}{x-5}\)

\(=\frac{x-5}{x\left(x-5\right)}-\frac{x}{x\left(x-5\right)}\)

\(=\frac{x-5-x}{x\left(x-5\right)}\)

\(=-\frac{5}{x\left(x-5\right)}\)

a: \(=49x^2-64-10\left(4x^2+12x+9\right)+5x\left(9x^2-12x+4\right)+4x\left(x^2-10x+25\right)\)

\(=49x^2-64-40x^2-120x-90+45x^3-60x^2+20x+4x^3-40x^2+100x\)

\(=49x^3-91x^2-154\)

b: \(=27x^3+189x^2+441x+343-125x^3+y^3+x^3+6x^2y+12xy^2+8y^3\)

\(=-97x^3+189x^2+441x+6x^2y+12xy^2+9y^3+343\)