Question

Simplify completely quantity x squared plus 4 x minus 45 all over x squared plus 10 x plus 9 and find the restrictions on the variable.

A) quantity x minus 5 over quantity x plus 1, x ≠ −1, x ≠ −9
B) quantity x minus 5 over quantity x plus 1, x ≠ −1, x ≠ 5
C) quantity x plus 5 over quantity x plus 1, x ≠ −1, x ≠ −9
D) quantity x plus 5 over x plus 1, x ≠ −1, x ≠ 5

Answer 1

A) Quantity x minus 5 over quantity x plus 1, where x≠-1 and x≠-9

Explanation:

`(x^2 + 4x - 45)/(x^2 + 10x + 9)`

Simplifying the numerator first:

x² + 4x - 45 using the quadratic formula you get;

(x - 5)(x + 9)

Then simplifying the denominator x² + 10x + 9 using a quadratic formula you get;

(x + 1)(x + 9)

Dividing the numerator and denominator now gives;

`((x - 5)(x + 9))/((x + 1)(x + 9))`

Cancelling (x + 9) throughout leaves you with;

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

The only restrictions here is if x = 1 and 9 which will give an undefined answer.