Question

I need you to solve this problem
$\frac{49 - x^{2} }{x {}^{2} - 14x + 49 }$
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Answer 1

${\texttt{\huge{\purple{SOLUTION :-}}}}$

GIVEN :-

$\frac{49 - x^{2} }{x {}^{2} - 14x + 49 }$

Firstly,

factorizing the numerator

$49 - {x}^{2} = {7}^{2} - {x}^{2}$

$49 - {x}^{2} = (7 - x)(7 + x)$

by using the formulae ⤵️

$\underline{ {a}^{2} - {b}^{2} = (a + b)(a - b)}$

Secondly,

factorizing the denominator

$x {}^{2} - 14x + 49 = {x}^{2} - (7 + 7)x + 49$

$x {}^{2} - 14x + 49 = {x}^{2} - 7x - 7x + 49$

$x {}^{2} - 14x + 49 = x(x - 7) - 7(x - 7)$

$x {}^{2} - 14x + 49 = (x - 7)(x - 7)$

NOW PUTTING ALL THE VALUES OF THE NUMERATOR AND THE DENOMINATOR...

$\frac{49 - x^{2} }{x {}^{2} - 14x + 49 } = \frac{(7 - x)(7 + x)}{(x - 7)(x - 7)}$

$\frac{49 - x^{2} }{x {}^{2} - 14x + 49 } = \frac{-(x - 7)(7 + x)}{(x - 7)(x - 7)}$

$\frac{49 - x^{2} }{x {}^{2} - 14x + 49 } = \frac{-(7 + x)}{(x - 7)}$

Answer....