\(A=\left(\frac{1+2x}{2.\left(2+x\right)}-\frac{x}{3.\left(x-2\right)}+\frac{2x^2}{3.\left(4-x^2\right)}\right).\frac{24-12x}{6+13x}\)

        \(=\left[\frac{3.\left(1+2x\right)\left(2-x\right)-2x\left(x+2\right)+4x^2}{2.3.\left(x+2\right)\left(2-x\right)}\right].\frac{24-12x}{6+13x}\)

          \(=\frac{6+9x-6x^2-2x^2-4x+4x^2}{6.\left(4-x^2\right)}.\frac{24-12x}{6+13x}\)

             \(=\frac{6+5x-4x^2}{6.\left(4-x^2\right)}.\frac{12.\left(2-x\right)}{6+13x}\) \(=\frac{\left(6+5x-4x^2\right).2}{\left(x+2\right)\left(6+13x\right)}=\frac{12+10x-8x^2}{13x^2+32x+12}\)

xem lại phân số cuối          

đúng đề òi ạ

Đề nghỉ ghi cái đề? @@ Rút gọn đúng ko?

\(Đkxđ:\hept{\begin{cases}x\ne\pm2\\x\ne-\frac{6}{13}\end{cases}}\)

\(A=\left[\frac{\left(1+2x\right)\left(x-2\right).3-2x\left(x+2\right)-4x^2}{6\left(x^2-4\right)}\right].\frac{12\left(2-x\right)}{6.13x}\)

\(=\left[\frac{3x-6+6x^2-12x-2x^2-4x-4x^2}{6\left(x^2-4\right)}\right].\frac{12\left(2-x\right)}{6+13x}\)

\(=\frac{13x+6}{6\left(x+2\right)\left(2-x\right)}.\frac{12\left(2-x\right)}{6+13x}\)

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

\(A=\left(\frac{1+2x}{4+2x}-\frac{x}{3x-6}+\frac{2x^2}{12-3x^2}\right)\times\frac{24-12x}{6+13x}\)

\(=\left(\frac{1+2x}{2\left(2+x\right)}+\frac{x}{3\left(2-x\right)}+\frac{2x^2}{3\left(4-x^2\right)}\right)\times\frac{2.\left(12-x\right)}{6+13x}\)

\(=\left(\frac{\left(1+2x\right).3.\left(2-x\right)}{2.3.\left(2+x\right)\left(2-x\right)}+\frac{2x\left(2+x\right)}{2.3.\left(2-x\right)\left(2+x\right)}+\frac{2.2x^2}{2.3.\left(2-x\right)\left(2+x\right)}\right)\times\frac{2.\left(12-x\right)}{6+13x}\)

\(=\left(\frac{6+12x-3x-6x^2+4x+2x^2+4x^2}{6\left(2-x\right)\left(2+x\right)}\right)\times\frac{2\left(12-x\right)}{6+13x}\)

\(=\frac{6+13x}{6\left(2-x\right)\left(2+x\right)}\times\frac{2\left(12-x\right)}{6+13x}\)

\(=\frac{12-x}{\left(2-x\right)\left(2+x\right)}=\frac{12-x}{4-x^2}\)

 ミ★๖ۣۜBăηɠ ๖ۣۜBăηɠ ★彡 Nếu đề bài là rút gọn thì đâu cần thì điều kiện xác định nha bạn!!

a,-0,162

Áp dụng  : \(\frac{1}{\sqrt{1}.2}< 2.\left(1-\frac{1}{\sqrt{2}}\right)\)

\(\frac{1}{\sqrt{2}.3}< 2.\left(\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}\right)\)

...................................

\(\frac{1}{\sqrt{2015}.2016}< 2.\left(\frac{1}{\sqrt{2015}}-\frac{1}{\sqrt{2016}}\right)\)

Cộng các BĐT trên với nhau được : \(\frac{1}{2}+\frac{1}{3\sqrt{2}}+\frac{1}{4\sqrt{3}}+...+\frac{1}{2016\sqrt{2015}}< 2\left(1-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{2015}}-\frac{1}{\sqrt{2016}}\right)=2\left(1-\frac{1}{\sqrt{2016}}\right)< 2\left(1-\frac{1}{\sqrt{2025}}\right)=\frac{88}{45}\)

Từ đó suy ra đpcm

Cái ............... là gì vậy bn

....................... là còn nữa đấy bạn :))