Question

Simplify the expression below.

Answer 1

Hello,

`(x+1)/(5x)`

with x ≠ 9

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)

`(x^(2) - 8 x-9)/(5x^(2) -45x) = ((x+1)(x-9))/(5 x (x-9)) = (x+1)/(5x)`

with x ≠ 9 because (x - 9) ≠ 0

Answer 2

`((x + 1 ))/(5 x)`

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) } \\ \\ = ((x + 1 ))/(5 x) \\`