Question

Wykonaj dzielenie zad 5,6bde,11
Funkcje wymierne

Answer 1

Zadanie 5:

a) [tex]\frac{8}{2x-9} : \frac{7}{4x-18} = \frac{8}{2x-9} * \frac{2(2x-9)}{7} = \frac{16}{7}[/tex]

b) [tex]\frac{-8}{3x-2} : \frac{2}{9x-6} = \frac{-8}{3x-2} * \frac{3(3x-2)}{2} = -12[/tex]

c) [tex]\frac{18}{2x-6} : \frac{-3}{4x-12} = \frac{18}{2x-6} * \frac{2(2x-6)}{-3} = -12[/tex]

d) [tex]\frac{-6}{3-2x} : \frac{9}{4x-6} = \frac{-6}{3-2x} * \frac{-2(3-2x)}{9} = 2[/tex]

e) [tex]\frac{9x}{2x+4} : \frac{6}{x+2} = \frac{9x}{2(x+2)} * \frac{x+2}{6} = \frac{9x}{12} = \frac{3}{4} x[/tex]

f) [tex]\frac{10x^{2}}{x-5} : \frac{5}{10-2x} = \frac{10x^{2}}{x-5} * \frac{-2(x-5)}{5} = \frac{-20x^{2}}{5} = -4x^{2}[/tex]

Zadanie 6:

b) [tex]\frac{2x + 4}{x-3} : \frac{3-x}{x+2} = \frac{2(x + 2)}{x-3} * \frac{x+2}{-(x-3)} = \frac{2(x+2)^{2}}{-(x-3)^{2}} = -2\frac{(x+2)^{2}}{(x-3)^{2}}[/tex]

d) [tex]\frac{6-4x}{(1-x)^{2}} : \frac{2x-3}{x-1} = \frac{-2(-3+2x)}{(1-x)^{2}} * \frac{-(-x+1)}{2x-3} = \frac{2}{1-x}[/tex]

e) [tex]\frac{x^{3}}{6x-2} : \frac{2x}{1-3x} = \frac{x^{3}}{-2(-3x+1)} * \frac{-3x+1}{2(x)} = \frac{x^{3}}{-2}* \frac{1}{2(x)} = -\frac{x^{2}}{4}[/tex]

Zadanie 11:

a) [tex]\frac{x^2{}-6x}{x+3} : \frac{x}{x+2} = \frac{x(x-6)}{x+3}*\frac{x+2}{x} = \frac{x-6}{x+3}*\frac{x+2}{1}=\frac{(x-6)(x+2)}{x+3}[/tex]

b) [tex]\frac{x}{6-x} : \frac{x^{2}+x}{x^{2}-36} = \frac{x}{-(x-6)}*\frac{(x-6)(x+6)}{x(x+1)} = -\frac{x+6}{x+1}[/tex]

c) [tex]\frac{x^{2}-1}{x^{2}+x} : \frac{x^{2}-2x+1}{x^{2}+1} = \frac{(x+1)(x-1)}{x(x+1)}*\frac{x^{2}+1}{(x-1)^{2}}=\frac{x^{2}+1}{x^{2}-x}[/tex]