Question

Simplify the expression below.

Answer 1

Answer:

$\frac{(x + 1 )}{5 x}$

Step-by-step explanation:

$\frac{ {x}^{2} - 8x - 9 }{5 {x}^{2} - 45x } \\ \\ = \frac{ {x}^{2} - 9x + x - 9 }{5 x({x} - 9) } \\ \\ = \frac{ x({x} - 9) + 1(x - 9 )}{5 x({x} - 9) } \\ \\ = \frac{ ({x} - 9) (x + 1 )}{5 x({x} - 9) } \\ \\ = \frac{(x + 1 )}{5 x}$

Answer 2

Answer:

Hello,

$\frac{x+1}{5x}$

with x ≠ 9

Step-by-step explanation:

a² - b² = (a + b) (a - b)

x² - 8 x - 9 = (x - 4)² - 16 - 9 = (x - 4)² - 25 = (x - 4)² - 5² = (x - 4 + 5) (x - 4 - 5)

= (x + 1) (x - 9)

5 x² - 45 x = 5 x  (x - 9)

$\frac{x^{2} - 8 x-9}{5x^{2} -45x} = \frac{(x+1)(x-9)}{5 x (x-9)} = \frac{x+1}{5x}$

with x ≠ 9  because  (x - 9) ≠ 0