Question

Rezolvati ecuatia: $\frac{5}{x+m}- \frac{1}{m-x} =2+ \frac{10m}{ m^{2}- x^{2} }$ . Mersi

Answer 1

Stabilim conditiile de existenta a ecuatiei:

x + m ≠ 0 ⇒x ≠ -m;  x - m ≠ 0 ⇒ x ≠ m

Deci, x ≠  ± m


[tex]\it...\Longleftrightarrow \dfrac{5}{m+x} -\dfrac{1}{m-x}-\dfrac{10m}{m^2-x^2} =2 \\\;\\ \Longleftrightarrow \dfrac{5m-5x-m-x-10m}{(m-x)(m+x)} =2 \\\;\\ \Longleftrightarrow \dfrac{-6m-6x}{(m-x)(m+x)} =2 \Leftrightarrow \dfrac{-6(m+x)}{(m-x)(m+x)} =2 \\\;\\ \Longleftrightarrow \dfrac{-6}{m-x}=2|_{:2} \Longleftrightarrow \dfrac{-3}{m-x} =1 \Longleftrightarrow -3=m-x \Longleftrightarrow x=m+3[/tex]

Answer 2

am preferat sa-ti trimit poza ca sa vezi mai bine amplificarile si simplificarile