Question

Bài 1: Tính a) (x - 4)/7 + (6x + 4)/7 b) + 3x+4 4-x 32 x²y² x²y c) (3x - 2)/(x + 1) - (2x - 1)/(x + 1) d) (x + y)/(3x) + (x - 2y)/(3x) Bài 2: Tính a) (x + 1)/(2x - 2) + (- 2x)/(x ^ 2 - 1) b) (x ^ 3 - 1)/(x ^ 2 - x) - (x ^ 3 + 1)/(x ^ 2 + x)

Answer 1

Bài 1

a) (x - 4)/7 + (6x + 4)/7

= (x - 4 + 6x + 4)/7

= 7x/7

= x

b) Đề thiếu

c) (3x - 2)/(x + 1) - (2x - 1)/(x + 1)

= (3x - 2 - x + 1)/(x + 1)

= (2x - 1)/(x + 1)

d) (x + y)/(3x) + (x - 2y)/(3x)

= (x + y + x - 2y)/(3x)

= (2x - y)/(3x)

Answer 2

Bài 2:

a: ĐKXĐ: \(x\notin\left\{1;-1\right\}\)

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

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

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

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

b: ĐKXĐ: \(x\notin\left\{0;1;-1\right\}\)

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

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

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

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