Question

giải phương trình chứa ẩn ở mẫu:

1) x+6/x-5 + x-5/x+6 = 2x^2+23x+61/x^2+x-30

2) 6/x-5 + x+2/x-8 = 18/(x-5)(8-x) - 1

3) x^2-x/x+3 - x^2/x-3 = 7x^2 - 3x/9-x^2

Answer 1

1: \(\dfrac{x+6}{x-5}+\dfrac{x-5}{x+6}=\dfrac{2x^2+23x+61}{x^2+x-30}\)

\(\Leftrightarrow x^2+12x+36+x^2-10x+25=2x^2+23x+61\)

=>23x+61=2x+61

hay x=0

2: \(\dfrac{6}{x-5}+\dfrac{x+2}{x-8}=\dfrac{18}{\left(x-5\right)\left(8-x\right)}-1\)

\(\Leftrightarrow6x-48+x^2-3x-10=-18-x^2+13x-40\)

\(\Leftrightarrow x^2+3x-58+x^2-13x+58=0\)

\(\Leftrightarrow2x^2-10x=0\)

=>2x(x-5)=0

=>x=0

c: \(\dfrac{x^2-x}{x+3}-\dfrac{x^2}{x-3}=\dfrac{7x^2-3x}{9-x^2}\)

\(\Leftrightarrow\left(x^2-x\right)\left(x-3\right)-x^2\left(x+3\right)=-7x^2+3x\)

\(\Leftrightarrow x^3-3x^2-x^2+3x-x^3-3x^2+7x^2-3x=0\)

\(\Leftrightarrow x^2=0\)

hay x=0