Question

giải phương trình
a) 8-x/x-7 - 8 = 1/x-7
b) x+5/x-5 - x-5/x+5 = 20/x^2 - 25

Answer 1

a) \(\dfrac{8-x}{x-7}-8=\dfrac{1}{x-7}\)(ĐKXĐ: \(x\ne7\))

\(\Leftrightarrow8-x-8\left(x-7\right)=1\)

\(\Leftrightarrow8-x-8x+56=1\)

\(\Leftrightarrow64-9x=1\)

\(\Leftrightarrow9x=63\)

\(\Leftrightarrow x=7\) (Không thỏa mãn ĐKXĐ)

Vậy...

b) \(\dfrac{x+5}{x-5}-\dfrac{x-5}{x+5}=\dfrac{20}{x^2-25}\)(ĐKXĐ: \(x\ne\pm5\))

\(\Leftrightarrow\left(x+5\right)\left(x+5\right)-\left(x-5\right)\left(x-5\right)=20\)

\(\Leftrightarrow\left(x+5\right)^2-\left(x-5\right)^2=20\)

\(\Leftrightarrow x^2+10x+25-\left(x^2-10x+25\right)=20\)

\(\Leftrightarrow x^2+10x+25-x^2+10x-25=20\)

\(\Leftrightarrow20x=20\)

\(\Leftrightarrow x=1\) (T/m ĐKXĐ)

Vậy....