Question

A, x/2x+6 - x/2x+2= 3x+2/(x+1)(x+3)

B, 5/x+7+8/2x+14= 2/3

C, x-1/x-1/x+1= 2x-1/x^2+x

Answer 1

a, \(\frac{x}{2x+6}+\frac{x}{2x-2}=\frac{3x+2}{\left(x+1\right)\left(x+3\right)}\) Đkxđ : \(x\ne-1;x\ne-3\)

⇌ x(x + 1) - x(x - 3) = 2(3x + 2)

⇌ x² + x - x² - 3x = 6x + 4

⇌ -8x = 4

⇌ x = \(-\frac{1}{2}\) ( tm đk)

→ S = \(\left\{-\frac{1}{2}\right\}\)

b, \(\frac{5}{x+7}+\frac{8}{2x+14}=\frac{2}{3}\) Đkxđ : \(x\ne-7\)

⇌ 30 + 24 = 2(x + 7)

⇌ 2x = 40

⇌ x = 20 (tmđk)

→ S = \(\left\{20\right\}\)

c, \(\frac{x-1}{\frac{x-1}{x+1}}=\frac{2x-1}{x^2+x}\) Đkxđ : \(x\ne-1\)

⇌ x = 2x - 1

⇌ x = 1 (tmđk)

→ S = \(\left\{1\right\}\)