Question

Cho biểu thức:

       P=[\(\frac{x-1}{x+1}\)-\(\frac{x}{x-1}\)-\(\frac{3x+1}{1-x^2}\)]:\(\frac{2x+1}{x^2}\)

a) Rút gọn biểu thức P.

b)Tìm các giá trị của x để P=\(\frac{3}{x-1}\)

c)Tìm x \(\in\)Z để P>1

Answer 1

\(P=\left(\frac{x-1}{x+1}-\frac{x}{x-1}-\frac{3x+1}{1-x^2}\right):\frac{2x+1}{x^2}\)
\(ĐKXĐ:x\ne\pm1;x\ne\frac{-1}{2}\)
\(a,P=\left[\frac{\left(x-1\right)^2}{\left(x+1\right)\left(x-1\right)}-\frac{x\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}+\frac{3x+1}{\left(x+1\right)\left(x-1\right)}\right]:\frac{2x+1}{x^2}\)
\(P=\left[\frac{x^2-2x+1-x^2-x+3x+1}{\left(x+1\right)\left(x-1\right)}\right]:\frac{2x+1}{x}\)
\(P=\frac{2}{\left(x+1\right)\left(x-1\right)}.\frac{x}{2x+1}\)

\(P=\frac{2x}{\left(x+1\right)\left(x-1\right)\left(2x+1\right)}\)