Question

please tell the answer step by step​

Answer 1

Answer:

$x = 10$

Step-by-step explanation:

$({x}^{2} - 14x + 49 )\div ( {x}^{2} - 49) = 3 \div 17$

First we solve LHS

${x}^{2} - 7x - 7x + 49 \div {x}^{2} - {7}^{2}$

$x(x - 7) - 7(x - 7) \div (x + 7)(x - 7)$

$x - 7 \div x + 7$

$(x - 7) \div (x + 7) = 3 \div 17$

$17(x - 7) = 3(x + 7)$

$17x - 119 = 3x + 21$

$17x - 3x = 21 + 119$

$14x = 140$

$x = 140 \div 14$

$x = 10$

there is only single value of x

Answer 2

Answer:

x=10

Step-by-step explanation:

x²- 14x + 49 / x²-49 = 3/17

x² - 2 (7×1)x + 7² / x² - 7² = 3/17                               (a-b)² = a² -2ab + b²

(x-7)² / (x+7)(x-7) = 3/17                                             a²-b² = (a+b)(a-b)

(x-7)(x-7) / (x+7)(x-7) = 3/17                                       (x-7)² = (x-7)(x-7)  

x-7 / x= 7 = 3 / 17                 {cutting x-7 from numerator and denominator}

17(x-7)= 3(x+7)                       {cross multiplication}

17x - 119 = 3x + 21                 {opening the bracket}

17x - 3x = 21 + 119                

14x = 140

x = 140/40

x = 10