Hvad er alle værdier af x: frac {2} {x + 6} + frac {2x} {x + 4} = frac {3x} {x + 6}?

Svar:

#COLOR (blå) (x = 4) farve (hvid) ("XX") orcolor (hvid) ("XX") farve (blå) (x = -2) #

Forklaring:

Givet

#COLOR (hvid) ("XXX") 2 / (x + 6) + (2x) / (x + 4) = (3x) / (x + 6) #

#rArr farve (hvid) ("XX") (2x) / (x + 4) = (3x-2) / (x + 6) #

krydsmultiplikation:

#color (hvid) ("XXX") (2x) xx (x + 6) = (3x-2) xx (x + 4) #

#rArrcolor (hvid) ("XX") 2x ^ 2 + 12x = 3x ^ 2 + 10x-8 #

#rArrcolor (hvid) ("XX") x ^ 2-2x-8 = 0 #

#rArrcolor (hvid) ("XX") (x-4) (x + 2) = 0 #

#rArr {:(x-4 = 0, farve (hvid) ("XX") orcolor (hvid) ("XX"), x + 2 = 0), (rarrx = 4, rarrx = -2):} #