Question

Hi there! I am so confused about these questions if anyone could help that would be great.

1. Simplify. x+5/x^2+6x+5
A) 1/x+1; where x= -1***
B) 1/x+1; where x=-1,-5
C) 1/x-5; where x=5
D) x-5

2. Simplify. x^2+3x-4/x+4
A) 1/x-4; where x=4
B) x-4
C) x-1; where x=1
D) x-1; where x=-4**

3. Simplify. 3/5a*1/a^2
A) 3/5a^2; where a=0
B) 3/5a^2
C) 3/5a^3; where a=0**
D) 4/5a^2; where a=0

I have chosen my answer with **, but I still would like to have someone check it because I am confused about the "where a=?". Thank you so much!

Answer 1

Your answers are correct.

Be careful with brackets on a site such as this.
e.g.
in #1 you will have to type it as
(x+5)/(x^2 + 6x + 5)
and your answer is 1/(x+1), x ≠ -1

As to the x ≠ ??

the concern is the denominator,
e.g. in #1, we have x+1 as a denominator.
What happens when x = -1 ?
We would be dividing by zero, which a mathematical NONO
For every other value of x , the denominator is just a non-zero number, so we can perform the division.

e.g. sub in x = 2
in the original:
= (2+5)/(4 + 12 + 5)
= 7/21
= 1/3

now sub in x = 2 into the simplified version
= 1/(2+1)
= 1/3 , that was much easier, that's why we simplified

The same is true for #2, the denominator is (x+4)
so x ≠ =4

in #3, the denominator is simply 5a^3, so a ≠ 0