Question

Rút gọn biểu thức: A=\(\frac{a^2+a-2}{a^{n+1}-3a^n}\times\left[\frac{\left(a+2\right)^2-a^2}{4a^2-4}-\frac{3}{a^2-a}\right]\)

Answer 1

bieu thuc nay ma rut xong chac mat day

Answer 2

\(=\frac{\left(a+2\right)\left(a-1\right)}{a^n\left(a-3\right)}.\left[\frac{\left(a+2-a\right)\left(a+2+a\right)}{4\left(a-1\right)\left(a+1\right)}-\frac{3}{a.\left(a-1\right)}\right]\) (Đk : x khác 0 ; 3 ; - 1 ; 1

\(=\frac{\left(a+2\right)\left(a-1\right)}{a^n\left(a-3\right)}.\left[\frac{4\left(a+1\right)}{4\left(a-1\right)\left(a+1\right)}-\frac{3}{a\left(a-1\right)}\right]\)

\(=\frac{\left(a+2\right)\left(a-1\right)}{a^n\left(a-3\right)}.\left[\frac{1}{a-1}-\frac{3}{a\left(a-1\right)}\right]\)

\(=\frac{\left(a+2\right)\left(a-1\right)}{a^n\left(a-3\right)}.\frac{a-3}{a\left(a-1\right)}=\frac{a+2}{a^{n+1}}\)

Answer 3

Ta có :

  \(A=\frac{a^2+a-2}{a^{n+1}-3a^n}\times\left[\frac{\left(a+2\right)^2-a^2}{4a^2-4}-\frac{3}{a^2-a}\right].\)

\(A=\frac{\left(a+2\right)\left(a-1\right)}{a^n\left(a-3\right)}.\left[\frac{\left(a+2-a\right)\left(a+2+a\right)}{4\left(a-1\right)\left(a+1\right)}-\frac{3}{a.\left(a-1\right)}\right]\)  \(ĐK:x\ne0;3;-1;1\)

\(A=\frac{\left(a+2\right)\left(a-1\right)}{a^n\left(a-3\right)}.\left[\frac{4\left(a+1\right)}{4\left(a-1\right)\left(a+1\right)}-\frac{3}{a.\left(a-1\right)}\right]\)

\(A=\frac{\left(a+2\right)\left(a-1\right)}{a^n.\left(a-3\right)}.\left[\frac{1}{a-1}-\frac{3}{a.\left(a-1\right)}\right]\)

\(A=\frac{\left(a+2\right).\left(a-1\right)}{a^n.\left(a-3\right)}.\frac{a-3}{a.\left(a-1\right)}\)

\(A=\frac{a+2}{a^{n+1}}\)

Answer 4

\(A=\frac{a^2+a-2}{a^{n+1}-3a^n}\times\left[\frac{\left(a+2\right)^2-a^2}{4a^2-4}-\frac{3}{a^2-a}\right]\)

\(A=\frac{a^2+a-2}{a^n.\left(a-3\right)}\times\left[\frac{\left(a+2-a\right)\left(a+2+a\right)}{\left(2a-2\right)\left(2a+2\right)}-\frac{3}{a.\left(a-1\right)}\right]\)

\(A=\frac{a^2+a-2}{a^n\left(a-3\right)}\times\left[\frac{2.\left(2a+2\right)}{2\left(a-1\right).2\left(a+1\right)}-\frac{3}{a\left(a-1\right)}\right]\)

\(A=\frac{a^2+a-2}{a^n.\left(a-3\right)}\times\left[\frac{2.2.\left(a+1\right)}{2.2.\left(a-1\right)\left(a+1\right)}-\frac{3}{a.\left(a-1\right)}\right]\)

\(A=\frac{a^2+a-2}{a^n.\left(a-3\right)}\times\left[\frac{1}{a-1}-\frac{3}{a\left(a-1\right)}\right]\)

\(A=\frac{a^2+a-2}{a^n.\left(a-3\right)}\times\left[\frac{a-3}{a\left(a-1\right)}\right]\)

\(A=\frac{a^2-1+a-1}{a^n.\left(a-3\right)}\times\frac{a-3}{a\left(a-1\right)}\)

\(A=\frac{\left(a-1\right)\left(a+1\right)+\left(a-1\right)}{a^n.\left(a-3\right)}\times\frac{a-3}{a\left(a-1\right)}\)

\(A=\frac{\left(a-1\right)\left(a+2\right)}{a^n.\left(a-3\right)}\times\frac{a-3}{a\left(a-1\right)}\)

\(A=\frac{a+2}{a^{n+1}}\)