[tex]{\texttt{\huge{\purple{SOLUTION :-}}}}[/tex]
GIVEN :-
[tex] \frac{49 - x^{2} }{x {}^{2} - 14x + 49 }[/tex]
Firstly,
factorizing the numerator
[tex]49 - {x}^{2} = {7}^{2} - {x}^{2} [/tex]
[tex]49 - {x}^{2} = (7 - x)(7 + x)[/tex]
by using the formulae ⤵️
[tex]\underline{ {a}^{2} - {b}^{2} = (a + b)(a - b)}[/tex]
Secondly,
factorizing the denominator
[tex]x {}^{2} - 14x + 49 = {x}^{2} - (7 + 7)x + 49[/tex]
[tex]x {}^{2} - 14x + 49 = {x}^{2} - 7x - 7x + 49[/tex]
[tex]x {}^{2} - 14x + 49 = x(x - 7) - 7(x - 7)[/tex]
[tex]x {}^{2} - 14x + 49 = (x - 7)(x - 7)[/tex]
NOW PUTTING ALL THE VALUES OF THE NUMERATOR AND THE DENOMINATOR...
[tex]\frac{49 - x^{2} }{x {}^{2} - 14x + 49 } = \frac{(7 - x)(7 + x)}{(x - 7)(x - 7)} [/tex]
[tex]\frac{49 - x^{2} }{x {}^{2} - 14x + 49 } = \frac{-(x - 7)(7 + x)}{(x - 7)(x - 7)} [/tex]
[tex]\frac{49 - x^{2} }{x {}^{2} - 14x + 49 } = \frac{-(7 + x)}{(x - 7)} [/tex]
Answer....
