Question

Can someone my answers

Simplify completely quantity x squared minus 10 x minus 24 all over x squared minus 3 x minus 108 and find the restrictions on the variable.
quantity x plus 2 over quantity x plus 9, x ≠ −2, x ≠ −9
quantity x plus 2 over quantity x plus 9, x ≠ −9, x ≠ 12
quantity x minus 2 over quantity x minus 9, x ≠ −2, x ≠ −9
quantity x minus 2 over quantity x minus 9, x ≠ −9, x ≠ 12

Answer 1

x + 2 over x + 9

x doesn’t equal to -9

x doesn’t equal to 12

Explanation:

Answer 2

Option 2 is correct that is
`(x+2)/(x+9)` and
`x\\eq-9`and
`x\\eq-12`

Explanation:

We have been given with the expression
`(x^2-10x-24)/(x^2-3x-108)`

We will simplify the given expression by factorisation we will get
`(x^2-12x+2x-24)/(x^2-12x+9x-108)`

Taking x as common from first two terms in numerator and 2 from last two terms in numerator

Similarly, take x common from first two terms and 9 from last two terms in denominator we will get

`(x(x-12)+2(x-12))/(x(x-12)+9(x-12))`

After arranging the terms we will get
`((x+2)(x-12))/((x+9)(x-12))`

Taking out the common factor which is (x-12) from numerator and denominator it will get cancelled we will get

`((x+2))/((x+9))`

Hence, Option 2 is correct that is
`(x+2)/(x+9)` and
`x\\eq-9`and
`x\\eq-12`