Question

giải các phương trình sau

a)\(\frac{4x-5}{x-1}=2+\frac{x}{x-1}\)

b)\(\frac{1}{x-2}+3=\frac{3-x}{x-2}\)

c)\(\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{16}{x^{ }2-1}\)

Answer 1

a) \(\frac{4x-5}{x-1}=\frac{2\left(x-1\right)}{x-1}+\frac{x}{x-1}\)

\(\Leftrightarrow4x-5-2x+2-x=0\)

\(\Leftrightarrow x=3\)

Vậy..

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

\(\Leftrightarrow1+3x-6-3+x=0\)

\(\Leftrightarrow4x=8\)

\(\Leftrightarrow x=2\)

Vậy...

c) \(\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{16}{x-1}\)

\(\Leftrightarrow\frac{\left(x+1\right)\left(x+1\right)-\left(x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=\frac{16\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}\)

\(\Leftrightarrow x^2+2x+1-x^2+2x-1-16x-16=0\)

\(\Leftrightarrow-12x=16\)

\(\Leftrightarrow x=-\frac{4}{3}\)

Vậy..