Explicație pas cu pas:
[tex]\frac{a}{b}=\frac{5}{4}[/tex]⇔[tex]a=\frac{5b}{4}[/tex]
a)[tex]\frac{3a+5b}{4a+b}=\frac{3\frac{5b}{4}+5b }{4\frac{5b}{4}+b } =\frac{\frac{15b}{4}+\frac{20b}{4} }{5b+b }=\frac{\frac{35b}{4} }{6b}=\frac{35b}{4}*\frac{1}{6b}=\frac{35b}{24b}=\frac{35}{24}[/tex]
b)[tex]\frac{9a-2b}{5a+3b}=\frac{9\frac{5b}{4}-2b}{5\frac{5b}{4}+3b}=\frac{\frac{45b}{4}-\frac{8b}{4} }{\frac{25b}{4}+\frac{12b}{4}}=\frac{45b-8b}{25b+12b}=\frac{37b}{37b}=1[/tex]
c)[tex]\frac{11a-9b}{2a\\+4b}=\frac{11\frac{5b}{4}-9b }{2\frac{5b}{4}+4b }=\frac{\frac{55b}{4}-\frac{36b}{4} }{\frac{10b}{4}+\frac{16b}{4} }=\frac{55b-36b}{10b+16b}=\frac{19b}{26b}=\frac{19}{26}[/tex]
d)[tex]\frac{6a-2b}{4a+3b}=\frac{6\frac{5b}{4}-2b }{4\frac{5b}{4}+3b }=\frac{\frac{30b}{4}-\frac{8b}{4} }{5b+3b}=\frac{\frac{22b}{4} }{8b}=\frac{11b}{2}*\frac{1}{8b}=\frac{11b}{16b}=\frac{11}{16}[/tex]
e)[tex]\frac{13a-11b}{4a+2b}=\frac{13\frac{5b}{4}-11b }{4\frac{5b}{4}+2b }=\frac{\frac{65b}{4}-\frac{44b}{4} }{5b+2b}=\frac{\frac{21b}{4} }{7b}=\frac{21b}{4}*\frac{1}{7b}=\frac{21b}{28b}=\frac{3}{4}[/tex]
f)[tex]\frac{a^{2}+b^{2} }{a^{2}-b^{2}}=\frac{(\frac{5b}{4})^{2}+b^{2} }{(\frac{5b}{4})^{2}-b^{2}}=\frac{\frac{25b^{2}}{16}+\frac{16b^{2}}{16} }{\frac{25b^{2}}{16}-\frac{16b^{2}}{16}}=\frac{\frac{41b^{2}}{16} }{\frac{9b^{2}}{16} }=\frac{41b^{2}}{9b^{2}}=\frac{41}{9}[/tex]
