Podaj konieczne założenia, wykonaj działanie [tex]\frac{3x^{2} +3x}{x^{2}-1 }[/tex] * [tex]\frac{x-1.... Question from @virus412

April 2022 2 9 Report

Podaj konieczne założenia, wykonaj działanie

[tex]\frac{3x^{2} +3x}{x^{2}-1 }[/tex] * [tex]\frac{x-1}{6x}[/tex]

Odpowiedź:

$\frac{3x^{2} +3x}{x^{2} -1}*\frac{x-1}{6x}=\frac{3x(x+1)}{x^{2}-1}*\frac{x-1}{3x*2}=\frac{(x+1)(x-1)}{2(x^{2} -1)}=\frac{x^{2} -1}{2(x^2-1)}=\frac{1}{2}\\x^{2} -1= 1(x^2-1)$

0 votes Thanks 1

unicorn05

x² - 1 ≠ 0 ∧ 6x ≠ 0

x ≠ 1 ∧ x ≠ -1 ∧ x ≠ 0

$\dfrac{3x^2+3x}{x^2-1}\cdot\dfrac{x-1}{6}=\dfrac{3x(x+1)}{(x-1)(x+1)}\cdot\dfrac{x-1}{6}=\dfrac{3x}{x-1}\cdot\dfrac{x-1}{6}=\dfrac{x}{1}\cdot\dfrac{1}{1}=x$

2 votes Thanks 1

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