Question

3) Simplify the expression and identify any restrictions on x. ​

Answer 1

`-(3x+14)/(x(x+5)(x-2))`

Explanation:

x² + 5x = x(x + 5)

x² + 3x - 10 = ( x + 5 )( x - 2 )

x² + 5x ≠ 0 , if x ≠ 0 or x ≠ - 5

x² + 3x - 10 ≠ 0 , if x ≠ - 5 or x ≠ 2

Restrictions are: x ≠ - 5, x ≠ 0, x ≠ 2

GCD is x(x + 5)(x - 2)

Given Expression =
`(7(x-2)+ 2x^2 - 2x(x+5))/(x(x+5)(x-2))` =

`(7x-14+2x^2 -2x^2 -10x)/(x(x+5)(x-2))` =

`-(3x+14)/(x(x+5)(x-2))`