Pismeni zadaci

Zadatak 0225

Test: MKsIIJAII_046

 

Reši jednačinu:

\(\frac{x(x+5)}{x^2-8x+12}+\frac{x+1}{x+7}=\frac{2x-2}{x+7}+\frac{12(x-1)}{x^2-8x+12}\)

 

Rešenje:


 

\(\frac{x(x+5)}{x^2-8x+12}+\frac{x+1}{x+7}=\frac{2x-2}{x+7}+\frac{12(x-1)}{x^2-8x+12}\)

\(\frac{x(x+5)}{x^2-8x+12}-\frac{12(x-1)}{x^2-8x+12}=\frac{2x-2}{x+7}-\frac{x+1}{x+7}\)

\(\frac{x^2+5x-12x+12}{x^2-8x+12}=\frac{2x-2-x-1}{x+7}\)

\(\frac{x^2-7x+12}{x^2-8x+12}=\frac{x-3}{x+7}\)

\((x^2-7x+12)(x+7)=(x-3)(x^2-8x+12)\)

\(x^3-7x^2+12x+7x^2-49x+84=x^3-8x^2+12x-3x^2+24x-36\)

\(11x^2-73x+120=0\)

\(x_{1,2}=\frac{73\pm \sqrt{5329-5280}}{22}=\frac{73\pm 7}{22}\)

\(x_{1}=\frac{40}{11}\),    \(x_{2}=3\).

 


 

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