Răspuns:
Explicație pas cu pas:
[tex]\frac{4a-3b}{5a-2b} = \frac{2}{3}[/tex]
[tex]3(4a-3b)= 2(5a-2b)[/tex]
[tex]12a - 9b = 10a - 4b[/tex]
[tex]12a - 10 a = -4b + 9b[/tex]
[tex]2a = 5b[/tex]
[tex]a= \frac{5b}{2}[/tex]
Asadar:
a)
[tex]\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[/tex]
b)
[tex]\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}[/tex]
