Answer:
x = 10
Step-by-step explanation:
Begin by factorising the numerator/ denominator of the left side
x² - 14x + 49 = (x - 7)² ← perfect square
x² - 49 = (x - 7)(x + 7) ← difference of squares
Thus left side becomes
[tex]\frac{(x-7)^2}{(x-7)(x+7)}[/tex] → x ≠ ± 7
Cancel (x - 7) on numerator/denominator, leaving
[tex]\frac{x-7}{x+7}[/tex]
Returning to the equation, that is
[tex]\frac{x-7}{x+7}[/tex] = [tex]\frac{3}{17}[/tex] ( cross- multiply )
17(x - 7) = 3(x + 7) ← distribute both sides
17x - 119 = 3x + 21 ( subtract 3x from both sides )
14x - 119 = 21 ( add 119 to both sides )
14x = 140 ( divide both sides by 14 )
x = 10
