1.
$P=\dfrac{x+2}{x^2+x+1}-\dfrac2{x-1}-\dfrac{2x^2+4}{1-x^3}$
$=\dfrac{x+2}{x^2+x+1}-\dfrac2{x-1}+\dfrac{2(x^2+2)}{(x-1)(x^2+x+1)}$
$=\dfrac{(x+2)(x-1)-2(x^2+x+1)+2(x^2+2)}{(x-1)(x^2+x+1)}$
$=\dfrac{x-2}{(x-1)(x^2+x+1)}$
$=\dfrac{x-2}{x^3-1}$
2.
$M=\dfrac1{3x-2}-\dfrac4{3x+2}-\dfrac{3x-6}{4-9x^2}$
$=\dfrac1{3x-2}-\dfrac4{3x+2}+\dfrac{3(x-2)}{(3x-2)(3x+2)}$
$=\dfrac{(3x+2)-4(3x-2)+3(x-2)}{(3x-2)(3x+2)}$
$=\dfrac{4-6x}{(3x-2)(3x+2)}$
$=\dfrac{2(2-3x)}{9x^2-4}$
5.
$L=\dfrac{x+1}{x-2}+\dfrac{2x}{x+2}+\dfrac{5x+2}{4-x^2}$
$=\dfrac{(x+1)(x+2)+2x(x-2)-(5x+2)}{(x-2)(x+2)}$
$=\dfrac{x^2+3x+2+2x^2-4x-5x-2}{(x-2)(x+2)}$
$=\dfrac{3x^2-6x}{(x-2)(x+2)}$
$=\dfrac{3x(x-2)}{(x-2)(x+2)}$
$=\dfrac{3x}{x+2}$
Vậy $L=\dfrac{3x}{x+2}$
6.
$Q=\left(\dfrac{2a}{a+3}+\dfrac{a+1}{a-3}+\dfrac{7a+3}{9-a^2}\right)\dfrac{(a+3)^2}{a}$
$=\left(\dfrac{2a}{a+3}+\dfrac{a+1}{a-3}-\dfrac{7a+3}{(a-3)(a+3)}\right)\dfrac{(a+3)^2}{a}$
$=\dfrac{2a(a-3)+(a+1)(a+3)-(7a+3)}{(a-3)(a+3)}\cdot\dfrac{(a+3)^2}{a}$
$=\dfrac{2a^2-6a+a^2+4a+3-7a-3}{(a-3)(a+3)}\cdot\dfrac{(a+3)^2}{a}$
$=\dfrac{3a^2-9a}{(a-3)(a+3)}\cdot\dfrac{(a+3)^2}{a}$
$=\dfrac{3a(a-3)}{(a-3)(a+3)}\cdot\dfrac{(a+3)^2}{a}$
$=3(a+3)$
Vậy $Q=3(a+3)$
3.
$N=\dfrac{x-1}{x+1}+\dfrac{x+1}{x-1}+\dfrac4{1-x^2}$
$=\dfrac{(x-1)^2+(x+1)^2-4}{(x-1)(x+1)}$
$=\dfrac{x^2-2x+1+x^2+2x+1-4}{x^2-1}$
$=\dfrac{2x^2-2}{x^2-1}$
$=\dfrac{2(x^2-1)}{x^2-1}$
$=2$
Vậy $N=2$
4.
$K=\left(\dfrac3{x^2-1}+\dfrac1{x+1}\right):\dfrac1{x+1}$
$=\left(\dfrac3{(x-1)(x+1)}+\dfrac1{x+1}\right)(x+1)$
$=\dfrac3{x-1}+1$
$=\dfrac{3+x-1}{x-1}$
$=\dfrac{x+2}{x-1}$
Vậy $K=\dfrac{x+2}{x-1}$
5.
\(L=\frac{\left(x+1\right)\left(x+2\right)+2x\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{\left(5x+2\right)}{x^2-4}\)
\(L=\frac{\left(x+1\right)\left(x+2\right)+2x\left(x-2\right)-5x-2}{\left(x-2\right)\left(x+2\right)}\)
\(L=\frac{x^2+3x+2+2x^2-4x-5x-2}{\left(x-2\right)\left(x+2\right)}\)
\(L=\frac{3x^2-6x}{\left(x-2\right)\left(x+2\right)}\)
\(L=\frac{3x\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(L=\frac{3x}{x+2}\)
6) \(Q=\left\lbrack\frac{2a\left(a-3\right)+\left(a+1\right)\left(a+3\right)}{\left(a-3\right)\left(a+3\right)}-\frac{\left(7a+3\right)}{a^2-9}\right\rbrack\cdot\frac{\left(a+3\right)^2}{a}\)
\(Q=\left\lbrack\frac{2a\left(a-3\right)+\left(a+1\right)\left(a+3\right)-7a-3}{\left(a-3\right)\left(a+3\right)}\right\rbrack\cdot\frac{\left(a+3\right)^2}{a}\)
\(Q=\left\lbrack\frac{2a^2-6a+a^2+4a+3-7a-3}{\left(a-3\right)\left(a+3\right)}\right\rbrack\cdot\frac{\left(a+3\right)^2}{a}\)
\(Q=\left\lbrack\frac{3a^2-9a}{\left(a-3\right)\left(a+3\right)}\right\rbrack\cdot\frac{\left(a+3\right)^2}{a}\)
\(Q=\frac{3a}{a+3}\cdot\frac{\left(a+3\right)^2}{a}\)
\(Q=3a+9\)
Bài \(1\):
\(P=\frac{x+2}{x^2+x+1}-\frac{2}{x-1}-\frac{2x^2+4}{1-x^3}\)
\(P=\frac{x+2}{x^2+x+1}-\frac{2}{x-1}-\frac{2x^2+4}{x^3-1}\)
\(P=\frac{\left(x+2\right)\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}-\frac{2\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}+\frac{2x^2+4}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(P=\frac{\left(x^2-x+2x-2\right)-\left(2x^2+2x+2\right)+2x^2+4}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(P=\frac{x^2+x-2-2x^2-2x-2+2x^2+4}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(P=\frac{\left(x^2-2x^2+2x^2\right)+\left(x-2x\right)+\left(-2-2+4\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(P=\frac{x^2-x}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(P=\frac{x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(P=\frac{x}{x^2+x+1}\)
Bài \(2\):
\(M=\frac{1}{3x-2}-\frac{4}{3x+2}-\frac{3x-6}{4-9x^2}\)
\(M=\frac{1}{3x-2}-\frac{4}{3x+2}-\frac{3x-6}{9x^2-4}\)
\(M=\frac{3x+2}{\left(3x-2\right)\left(3x+2\right)}-\frac{4\left(3x-2\right)}{\left(3x-2\right)\left(3x+2\right)}+\frac{3x-6}{\left(3x-2\right)\left(3x+2\right)}\)
\(M=\frac{\left(3x+2\right)-\left(12x-8\right)\left(3x+6\right)}{\left(3x-2\right)\left(3x+2\right)}\)
\(M=\frac{3x+2-12x+8+3x-6}{\left(3x-2\right)\left(3x+2\right)}\)
\(M=\frac{\left(3x-12x+3x\right)\left(2+8-6\right)}{\left(3x-2\right)\left(3x+2\right)}\)
\(M=\frac{-6x+4}{\left(3x-2\right)\left(3x+2\right)}\)
\(M=\frac{-2\left(3x-2\right)}{\left(3x-2\right)\left(3x+2\right)}\)
\(M=\frac{-2}{3x+2}\)
Còn mấy bài sau áp dụng y chang bạn tự làm nhé!
