Simplify completely quantity 12 x plus 36 over quantity x squared minus 4 x minus 21 and find the restrictions on the variable.

a.) 12 over quantity x minus 7, x ≠ 7
b.) 12 over quantity x minus 7, x ≠ 7, x ≠ −3
c.) quantity x plus 3 over quantity x minus 7, x ≠ 7
d.)quantity x plus 3 over quantity x minus 7, x ≠ 7, x ≠ −3

Option B

12 over quantity x minus 7, x ≠ 7, x ≠ −3

Solution:

Given that we have to simplify quantity 12 x plus 36 over quantity x squared minus 4 x minus 21

So we have to simplify,

We have to find the restrictions on the variable

The above given Rational function is defined, for

In order to simplify the above expression, we need to factor both the numerator and the denominator

For the denominator, we need to split the middle term of the quadratic to get factored form,

Fcatoring the denominator part,

Cancel out common factors to get,

Thus option B is correct. 12 over quantity x minus 7, x ≠ 7, x ≠ −3

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3

2,600 divided by 80 = 32.5

step-by-step explanation: