Question

URGENT VA ROGG!!!
6) Efectuați :
a) 5x/9 + 2x/9 ;
b) x/y + 5x/y - 12x/y
c) 4x+1/3a - 4x-2y-3/3a + 5x+y/3a
d) 5x/6 - 3y/4 + y/2 - 2x/3
e) x+2/14 - 2x-1/2 + x-2/7
f) 3a/6ax^2 - x/6a^2x + a/3a^2x^2

Answer 1

Răspuns:

Explicație pas cu pas:

Vom folosi urmatoarele formule:

$\displaystyle\boxed{\frac{a}{y} +\frac{b}{y} =\frac{a+b}{y}} \\\displaystyle\boxed{\frac{a}{y} -\frac{b}{y} =\frac{a-b}{y} }$

Trecem la efectuarea calculelor

a)

$\displaystyle\frac{5x}{9} +\frac{2x}{9} =\frac{5x+2x}{9} =\frac{7x}{9}$

b)

$\displaystyle\frac{x}{y} +\frac{5x}{y} -\frac{12x}{y} =\frac{x+5x-12x}{y} =\frac{-6x}{y}$

c)

$\displaystyle\frac{4x+1}{3a} -\frac{4x-2y-3}{3a} +\frac{5x+y}{3a} =\frac{\not4x+1-\not4x+2y+3+5x+y}{3a} =\frac{5x+3y+4}{3a}$

d)

Daca observam nu putem sa aplicam formula de mai sus deoarece nu avem   numitorul comun

Ca sa aflam numitorul comun incercam sa aflam cel mai mic multiplu comun

Ca sa aflam acest lucru trecem la descompunerea numerelor dupa care vom lua numerele comune si necomune la puterea cea mai mare

6=2x3

4=2²

2=2

3=1

c.m.m.m.c=2²x34x3=12

$\displaystyle\frac{5x}{6} -\frac{3y}{4} +\frac{y}{2} -\frac{2x}{3} =\frac{2\times5x}{12} -\frac{3\times3y}{12} +\frac{6\times y}{12} -\frac{4\times 2x}{12} =\frac{10x-9y+12y-8x}{12} =\frac{2x-3y}{12}$

e)

14=7x2

2=2

7=7

------------

c.m.m.m.c=7x2=14

$\displaystyle\frac{x+2}{14} -\frac{2x-1}{2} +\frac{x-2}{7} =\frac{x+2}{14} -\frac{7(2x-1)}{14} +\frac{2(x-2)}{14} =\frac{x+\not2-14x+7+2x-\not2}{14} =\frac{7-11x}{14}$

f) observam ca factorul comun este 6a^2x^2

$\displaystyle\frac{3a}{6ax^{2} } -\frac{x}{6a^{2}x } +\frac{a}{3a^{2}x^{2} } =\frac{3a\times a}{6a^{2} x^{2} } -\frac{x\times x}{6a^{2}x^{2} } +\frac{a\times 2}{6a^{2}x^{2} } =\frac{3a^{2}-x^{2}+2a }{6a^{2}x^{2} }$