Wyrażenia wymierne

[luukasz1]

1. Wykonaj działania.

a)\(\frac{3}{x*2-25}\) - \(\frac{x+2}{5-x}\)+4
b)5-\(\frac{1}{x+2}\)
c)\(\frac{7}{1-x\) - 4
d)\(\frac{1}{x-1}\) - \(\frac{2}{x^2-1}\)

[jola]

a.
\(x \neq 5\ \ \ \wedge \ \ \ x \neq -5\)

\(\frac{3}{x^2-25} -\ \frac{x+2}{5-x} \ +\ 4\ =\ \frac{3}{(x-5)(x+5)}\ +\ \frac{x+2}{x-5} \ +\ 4\ =\ \frac{3+(x+2)(x+5)+4(x^2-25)}{(x-5)(x+5)}\ =\\)

\(=\ \frac{3+x^2+7x+10+4x^2-100}{(x-5)(x+5)}\ =\ \frac{5x^2+7x-87}{(x-5)(x+5)}\)

[jola]

b.
\(x \neq -2\)

\(5\ -\ \frac{1}{x+2}\ =\ \frac{5x+10-1}{x+2}\ =\ \frac{5x+9}{x+2}\)

[jola]

c.
\(x \neq 1\)

\(\frac{7}{1-x} -4\ =\ \frac{7-4+4x}{1-x}\ =\ \frac{3+4x}{1-x}\)

[jola]

d.
\(x \neq 1\ \ \ \wedge \ \ \ x \neq -1\)

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