Question

Please solve these two questions

Answer 1

Question 4

Simplifying the expression
`(x^2-10x-24)/(x^2-3x-108)` we get
`(x-2)/(x-9)` and x≠9 or x≠2

Option D is correct option.

Question 5

Simplifying the expression:
`(8x-16)/(x^2-13x+22)` we get
`(8)/(x-11), x\\eq 11`

Option C is correct.

Explanation:

Question 4

Simplify completely
`(x^2-10x-24)/(x^2-3x-108)`

For simplifying the above expression we have to find find factors of numerators and denominators

First finding factors of numerator
`x^2-10x-24`

`x^2-10x-24\\ = x^2-12x+2x-24 \\= x(x-12)+2(x-12) \\=(x-12)(x-2)`

So, the factors of
`x^2-10x-24` are
`(x-12)(x-2)`

Now finding factors of denominator
`x^2-3x-108`

`x^2-3x-108\\=x^2-12x+9x-108\\=x(x-12)+9(x-12)\\=(x+9)(x-12)`

So, factors of
`x^2-3x-108 are (x-12)(x+9)`

Now, replacing numerators and denominators with their factors

`(x^2-10x-24)/(x^2-3x-108)\\=((x-12)(x-2))/((x+9)(x-12))\\Cancelling\:(x-12) \: from\:numerator\:and\:denominator\\=(x-2)/(x-9)`

so, simplifying the expression
`(x^2-10x-24)/(x^2-3x-108)` we get
`(x-2)/(x-9)` and x≠9 or x≠2

Option D is correct option.

Question No 5

Simplify the expression:
`(8x-16)/(x^2-13x+22)`

For simplifying the above expression we have to find find factors of numerators and denominators

First finding factors of numerator
`8x-16`

Taking 8 common:

`8x-16\\=8(x-2)`

So, factors of
`8x-16` are
`8(x-2)`

Now finding factors of denominator :
`x^2-13x+22`

`x^2-13x+22\\=x^2-11x-2x+22\\=x(x-11)-2(x-11)\\=(x-2)(x-11)`

Now, replacing numerators and denominators with their factors

`(8x-16)/(x^2-13x+22)\\=(8(x-2))/((x-11)(x-2))\\Cancelling\:(x-2)\\=(8)/(x-11), x\\eq 11`

So, simplifying the expression:
`(8x-16)/(x^2-13x+22)` we get
`(8)/(x-11), x\\eq 11`

Option C is correct.