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 } = ((7 - x)(7 + x))/((x - 7)(x - 7))`

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

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

Answer....