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

Step-by-step explanation:

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

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

Step-by-step explanation:

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;

Cancelling (x + 9) throughout leaves you with;

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

step-by-step explanation:

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|