September 2018 0 21 Report

1) podaj dziedzinę wyrazenia a nastepnie je uprość:

a)\frac{x^{3} +7x^{2}}{x+7}

b)\frac{5x-15}{x^{2}-3x

c)\frac{x^{2}+2x}{x{^{3}-4x

d)\frac\frac{x^{3}+x}{x^{4}-1

e)\\frac{x^{2}+10x+25}{x^3+5x^2}

f)\frac{3x^3+3x^2}{x^4+2x^3+x^2

g)\\frac{9-x^2}{x^2-6x+9}

h)\frac{4x^2-1}{4x^2-4x+1

Reklama

Odpowiedzi

abcdefghh
abcdefghh

a) Df=R\{-7}

\frac{5x-15}{x^2-3x}=\frac{5(x-3)}{x(x-3)}=\frac{5}{x}

c)x³-4x≠0

x(x²-4)≠0

x≠0 x≠2 x≠-2

Df=R\{-2,0,2}

\frac{x^{2}+2x}{x^{3}-4x}=\frac{x(x+2)}{x(x^2-4)}=\frac{x(x+2)}{x(x-2)(x+2)}=\frac{1}{x-2}

d)

x⁴-1≠0

x⁴≠1

x≠1

Df=R\{1}

\frac{x^{3}+x}{x^4-1}=\frac{x(x^2+1)}{(x^2+1)(x^2-1)}=\frac{x}{x^2-1}

e)

x³+5x²≠0

x²(x+5)≠0

x≠0 x≠-5

Df=R\{-5,0}

\frac{x^{2}+10x+25}{x^3+5x^2}=\frac{(x+5)(x+5)}{x^2(x+5)}=\frac{x+5}{x^2}

f)

x⁴+2x³+x²≠0

x²(x²+2x+1)≠0

x≠0 x≠-1

Df=R\{-1,0}

\frac{3x^3+3x^2}{x^4+2x^3+x^2}=\frac{3x^2(x+1)}{x^2(x+1)(x+1)}=\frac{3x^2}{x^2(x+1)}

g)

Df=R\{3}

\frac{9-x^2}{x^2-6x+9}=\frac{(3-x)(3+x)}{(x-3)(x-3)}=\frac{(x-3)(-x-3)}{(x-3)(x-3)}=\frac{-x-3}{x-3}

h)

Df=R\{½}

\frac{4x^2-1}{4x^2-4x+1}=\frac{(2x-1)(2x+1)}{(2x-1)^2}=\frac{2x+1}{2x-1}


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