Question

[nguyễn thị thanh ngân]

rút gọn biểu thức A=\(x/x-1+3/x+1+3-5*x/x^2-1\) với x<>-1;1

Answer 1

[l҉o҉n҉g҉ d҉z҉]

\(A=\frac{x}{x-1}+\frac{3}{x+1}-\frac{5x}{x^2-1}\)

\(=\frac{x\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{3\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}-\frac{5x}{\left(x-1\right)\left(x+1\right)}\)

\(=\frac{x^2+x}{\left(x-1\right)\left(x+1\right)}+\frac{3x-3}{\left(x-1\right)\left(x+1\right)}-\frac{5x}{\left(x-1\right)\left(x+1\right)}\)

\(=\frac{x^2+x+3x-3-5x}{\left(x-1\right)\left(x+1\right)}=\frac{x^2-x-3}{\left(x-1\right)\left(x+1\right)}\)