Question

giải các phương trình

a)\(\frac{4x-3}{x-5}=\frac76\)

b)\(\frac{2x+5}{2x}-\frac{x}{x+5}=0\)

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

Answer 1

a: ĐKXĐ: x<>5

Ta có: \(\frac{4x-3}{x-5}=\frac76\)

=>\(6\left(4x-3\right)=7\left(x-5\right)\)

=>24x-18=7x-35

=>17x=-35+18=-17

=>x=-1(nhận)

b: ĐKXĐ: x∉{0;-5}

Ta có: \(\frac{2x+5}{2x}-\frac{x}{x+5}=0\)

=>\(\frac{\left(2x+5\right)\left(x+5\right)-2x\cdot x}{2x\left(x+5\right)}=0\)

=>\(\left(2x+5\right)\left(x+5\right)-2x^2=0\)

=>\(2x^2+10x+5x+25-2x^2=0\)

=>15x=-25

=>\(x=-\frac{25}{15}=-\frac53\) (nhận)

c: ĐKXĐ: x<>1

Ta có: \(\frac{4x-5}{x-1}=2+\frac{x}{x-1}\)

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

=>4x-5=3x-2

=>4x-3x=-2+5

=>x=3(nhận)