Ответ:

[tex]\frac{a^{2}+5a-14 }{a^{2}+14a+49 } =\frac{(a-2)(a+7)}{(a+7)^{2} } =\frac{a-2}{a+7}[/tex]

[tex]a^{2}+5a-14=0[/tex]

[tex]D=b^{2} -4ac=5^{2} -4*1*(-14)=25+56=81[/tex]

[tex]a_{1,2} =\frac{-bб\sqrt{D} }{2a}[/tex]

[tex]a_{1} =\frac{-5+\sqrt{81} }{2} =\frac{-5+9}{2}=\frac{4}{2} =2[/tex]

[tex]a_{2} =\frac{-5-\sqrt{81} }{2} =\frac{-5-9}{2}=\frac{-14}{2} =-7[/tex]

[tex]a^{2} +5a-14=(a-2)(a+7)[/tex]

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[tex]a^{2} +14a+49=0[/tex]

[tex]D=b^{2} -4ac=14^{2} -4*1*49=196-196=0[/tex]

[tex]a=\frac{-b}{2a}[/tex]

[tex]a=\frac{-14}{2}=-7[/tex]

[tex]a^{2} +14a+49=(a+7)^{2}[/tex]