Answer:
Question 4
Simplifying the expression [tex]\frac{x^2-10x-24}{x^2-3x-108}[/tex] we get [tex]\frac{x-2}{x-9}[/tex] and x≠9 or x≠2
Option D is correct option.
Question 5
Simplifying the expression: [tex]\frac{8x-16}{x^2-13x+22}[/tex] we get [tex]\frac{8}{x-11}, x\neq 11[/tex]
Option C is correct.
Step-by-step explanation:
Question 4
Simplify completely [tex]\frac{x^2-10x-24}{x^2-3x-108}[/tex]
For simplifying the above expression we have to find find factors of numerators and denominators
First finding factors of numerator [tex]x^2-10x-24[/tex]
[tex]x^2-10x-24\\ = x^2-12x+2x-24 \\= x(x-12)+2(x-12) \\=(x-12)(x-2)[/tex]
So, the factors of [tex]x^2-10x-24[/tex] are [tex](x-12)(x-2)[/tex]
Now finding factors of denominator [tex]x^2-3x-108[/tex]
[tex]x^2-3x-108\\=x^2-12x+9x-108\\=x(x-12)+9(x-12)\\=(x+9)(x-12)[/tex]
So, factors of [tex]x^2-3x-108 are (x-12)(x+9)[/tex]
Now, replacing numerators and denominators with their factors
[tex]\frac{x^2-10x-24}{x^2-3x-108}\\=\frac{(x-12)(x-2)}{(x+9)(x-12)}\\Cancelling\:(x-12) \: from\:numerator\:and\:denominator\\=\frac{x-2}{x-9}[/tex]
so, simplifying the expression [tex]\frac{x^2-10x-24}{x^2-3x-108}[/tex] we get [tex]\frac{x-2}{x-9}[/tex] and x≠9 or x≠2
Option D is correct option.
Question No 5
Simplify the expression: [tex]\frac{8x-16}{x^2-13x+22}[/tex]
For simplifying the above expression we have to find find factors of numerators and denominators
First finding factors of numerator [tex]8x-16[/tex]
Taking 8 common:
[tex]8x-16\\=8(x-2)[/tex]
So, factors of [tex]8x-16[/tex] are [tex]8(x-2)[/tex]
Now finding factors of denominator : [tex]x^2-13x+22[/tex]
[tex]x^2-13x+22\\=x^2-11x-2x+22\\=x(x-11)-2(x-11)\\=(x-2)(x-11)[/tex]
Now, replacing numerators and denominators with their factors
[tex]\frac{8x-16}{x^2-13x+22}\\=\frac{8(x-2)}{(x-11)(x-2)}\\Cancelling\:(x-2)\\=\frac{8}{x-11}, x\neq 11[/tex]
So, simplifying the expression: [tex]\frac{8x-16}{x^2-13x+22}[/tex] we get [tex]\frac{8}{x-11}, x\neq 11[/tex]
Option C is correct.
