bài 6:
\(A = \frac{20(x^2 + 6x + 9)}{(3x+5-2x)(3x+5+2x)} + \frac{5(x^2 - 25)}{(3x-2x-5)(3x+2x+5)} - \frac{(2x+3-x)(2x+3+x)}{3(x+3)(x+5)}\)
\(A = \frac{20(x+3)^2}{(x+5)(5x+5)} + \frac{5(x-5)(x+5)}{(x-5)(5x+5)} - \frac{(x+3)(3x+3)}{3(x+3)(x+5)}\)
\(A = \frac{20(x+3)^2}{5(x+5)(x+1)} + \frac{5(x-5)(x+5)}{5(x-5)(x+1)} - \frac{3(x+3)(x+1)}{3(x+3)(x+5)}\)
\(A = \frac{4(x+3)^2}{(x+5)(x+1)} + \frac{x+5}{x+1} - \frac{x+1}{x+5}\)
\(A = \frac{4(x^2 + 6x + 9) + (x+5)^2 - (x+1)^2}{(x+5)(x+1)}\)
\(A = \frac{4x^2 + 24x + 36 + x^2 + 10x + 25 - (x^2 + 2x + 1)}{(x+5)(x+1)}\)
\(A = \frac{4x^2 + 32x + 60}{(x+5)(x+1)}\)
\(A = \frac{4(x^2 + 8x + 15)}{(x+5)(x+1)}\)
\(A = \frac{4(x+3)(x+5)}{(x+5)(x+1)}\)
\(A = \frac{4(x+3)}{x+1}\)
bài 7:
\(P = \frac{6x^2 + 8x + 7}{(x-1)(x^2 + x + 1)} + \frac{x}{x^2 + x + 1} - \frac{6}{x-1}\)
\(P = \frac{6x^2 + 8x + 7 + x(x-1) - 6(x^2 + x + 1)}{(x-1)(x^2 + x + 1)}\)
\(P = \frac{6x^2 + 8x + 7 + x^2 - x - 6x^2 - 6x - 6}{(x-1)(x^2 + x + 1)}\)
\(P = \frac{x^2 + x + 1}{(x-1)(x^2 + x + 1)}\)
\(P = \frac{1}{x-1}\)
Thay \(x = \frac{1}{2}\) vào biểu thức ta được:
\(P = \frac{1}{\frac{1}{2} - 1}\)
\(P = \frac{1}{-\frac{1}{2}}\)
\(P = -2\)
bài 8:
\(P = \frac{10}{(x+2)(3-x)} - \frac{12}{(3-x)(3+x)} - \frac{1}{(x+3)(x+2)}\)
\(P = \frac{10(x+3) - 12(x+2) - 1(3-x)}{(x+2)(3-x)(x+3)}\)
\(P = \frac{10x + 30 - 12x - 24 - 3 + x}{(x+2)(3-x)(x+3)}\)
\(P = \frac{-x + 3}{(x+2)(3-x)(x+3)}\)
\(P = \frac{3-x}{(x+2)(3-x)(x+3)}\)
\(P = \frac{1}{(x+2)(x+3)}\)
Thay \(x = -0,75 = -\frac{3}{4}\) vào biểu thức:
\(P = \frac{1}{(-0,75 + 2)(-0,75 + 3)}\)
\(P = \frac{1}{1,25 \cdot 2,25}\)
\(P = \frac{1}{\frac{5}{4} \cdot \frac{9}{4}} = \frac{1}{\frac{45}{16}} = \frac{16}{45}\)
bài 9:
\(A = \frac{x+1}{x-1} + \frac{x-1}{x+1} - \frac{4}{x^2 - 1}\)
\(A = \frac{(x+1)^2}{(x-1)(x+1)} + \frac{(x-1)^2}{(x-1)(x+1)} - \frac{4}{(x-1)(x+1)}\)
\(A = \frac{x^2 + 2x + 1 + x^2 - 2x + 1 - 4}{(x-1)(x+1)}\)
\(A = \frac{2x^2 - 2}{x^2 - 1}\)
\(A = \frac{2(x^2 - 1)}{x^2 - 1}\)
\(A = 2\)
bài 10:
\(x + \frac{1}{a^2 - a} = \frac{a}{a - 1}\)
\(x = \frac{a}{a - 1} - \frac{1}{a^2 - a}\)
\(x = \frac{a}{a - 1} - \frac{1}{a(a - 1)}\)
\(x = \frac{a^2 - 1}{a(a - 1)}\)
\(x = \frac{(a-1)(a+1)}{a(a-1)}\)
\(x = \frac{a+1}{a}\)
