Zadání:
Vypočítejte následující rovnici (v množině R):
$$\frac{x+7}{2x+2}-\frac{x+4}{4x+4}=1$$
Řešení:
Začneme tím, že si upravíme oba jmenovatele:
$$\frac{x+7}{2(x+1)}-\frac{x+4}{4(x+1)}=1$$
V tuto chvíli si stanovíme i podmínku, že x≠-1 (jinak by byla ve jmenovateli nula, což nejde)
Nyní celou rovnici vynásobíme výrazem 4(x+1) a dostaneme:
$$2(x+7)-(x+4)=4(x+1)$$
Upravíme a získáme:
$$2x+14-x-4=4x+4$$
$$x+10=4x+4$$
$$3x=6$$
$$x=2$$
K={2}
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