I need you to solve this problem \frac{49 - x^(2) }{x {}^(2) - 14x + 49 }

Question

asked Jan 16, 2020 221k views

1 Answer

CEeNiKc · Answer 1 · 2020-01-20T02:59:37+0000

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

GIVEN :-

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

factorizing the numerator

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

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

by using the formulae ⤵️

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

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....