Question

Giải các phương trình:

\(a,\dfrac{5x^2+16}{x^2-16}=\dfrac{2x-1}{x+4}-\dfrac{3x-1}{4-x}\)

\(b,\dfrac{y+1}{y-2}-\dfrac{5}{y+2}=\dfrac{12}{y^2-4}+1\)

Answer 1

a)

\(\dfrac{5x^2+16}{x^2-16}=\dfrac{2x-1}{x+4}-\dfrac{3x-1}{4-x}\) (\(x\ne\pm2\))

\(\Rightarrow\dfrac{5x^2+16}{\left(x-4\right)\left(x+4\right)}-\dfrac{\left(2x-1\right)\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}-\dfrac{\left(3x-1\right)\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}=0\)

\(\Rightarrow\dfrac{5x^2+16-\left(2x^2-8x-x+4\right)-\left(3x^2+12x-x-4\right)}{\left(x-4\right)\left(x+4\right)}=0\)

\(\Rightarrow\dfrac{10x+16}{x^2-16}=0\)

=> 10x + 16 =0

=> 10x = -16

=> x = \(-\dfrac{8}{5}\)