Question

daca 4a-3b/5a-2b egal 2/3 , calculati valoarea rapoartelor :
a) 2a+b/a-b
b)a la puterea a doua - ab/ b la puterea 2 + ab
dau 100pct plus coroana
rapid
va rog

Answer 1

Răspuns:

Explicație pas cu pas:

(4a-3b)/(5a-2b) = 2/3 <=>

2·(5a-2b) = 3· (4a-3b) <=>

10a - 4b = 12a - 9b => 12a - 10a = 9b-4b =>

2a = 5b => a = 5b/2

(2a+b)/(a-b) = (5b+b)/(5b/2 -b) = 6b/ (3b/2) = 12b/3b = 4

(a²-ab)/(b²+ab) = (25b²/4 - ²⁾5b²/2) /(²⁾b²+5b²/2) =

= (15b²/4)/(7b²/2) = (15b²·2)/(4·7b²) = 15/14

Answer 2

Răspuns:

Explicație pas cu pas:

$\frac{4a-3b}{5a-2b} = \frac{2}{3}$

$3(4a-3b)= 2(5a-2b)$

$12a - 9b = 10a - 4b$

$12a - 10 a = -4b + 9b$

$2a = 5b$

$a= \frac{5b}{2}$

Asadar:

a)

$\frac{2a+b}{a-b} = \frac{2\frac{5b}{2} +b }{\frac{5b}{2} -b} = \frac{5b+b}{\frac{5b-2b}{2}} = \frac{6b}{\frac{3b}{2}} = \frac{12b}{3b} = 4$

b)

$\frac{a^{2}-ab }{b^{2}+ab } = \frac{ (\frac{5b}{2})^{2}- \frac{5b}{2}b }{b^{2}+ \frac{5b}{2}b } = \frac{ \frac{25b^{2} }{4}- \frac{5b^{2} }{2}}{b^{2}+ \frac{5b^{2} }{2} } = = \frac{ \frac{25b^{2}-10b^{2} }{4}}{\frac{2b^{2} + 5b^{2} }{2} } = \frac{ \frac{15b^{2}}{4}}{\frac{7b^{2}}{2} } =\frac{ 15b^{2}}{2(7b^{2}) } = \frac{ 15b^{2}}{14b^{2}} =\frac{15}{14}$