Question

solve the following questions

Answer 1

given,
      x+7   -  9        
       5          x-2
=    (x+7)(x-2) -45
              5(x-2)
=  x²-2x+7x-14-45
            5x-10
=  x²+5x-59    -1
        5x-10

⇒ x²+5x-59 = 5x -10
⇒x²-59+10  = 0
⇒x² -49      =  0
⇒(x+7)(x-7) = 0    since (a² -b²) = (a+b)(a-b)
⇒x = +7, -7

Answer 2

$\frac{x+7}{5}$ - $\frac{9}{x-2}$ = 1

$\frac{(x+7)(x-2) - 45}{5(x-2)}$ = 1

$\frac{x^{2} -2x +7x -14 -45}{5x-10} = 1$

x² + 5x - 59 = 5x - 10

x² -49 = 0

x = 7 and -7