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

you already gave the answer

step-by-step explanation:

c. 6tan80

step-by-step explanation: