Which expression is equivalent to(q4)-3/q-15 for all values of q where the expression is defined?
answer choices
q27
1/q27
q3
1/q3
1/q3
Show your work
To simplify the expression (q^4 - 3)/(q - 15), we first factor out q^4 - 3 using the difference of squares formula. The difference of squares formula states that a^2 - b^2 = (a + b)(a - b).
So, q^4 - 3 = (q^2)^2 - (sqrt(3))^2 = (q^2 + sqrt(3))(q^2 - sqrt(3)).
Therefore, our expression becomes (q^2 + sqrt(3))(q^2 - sqrt(3))/(q - 15).
Next, we try to simplify the expression further to get our final answer:
[(q + sqrt(3))(q - sqrt(3))]/(q - 15).
By cancelling out the (q - sqrt(3)) terms in the numerator and denominator, we get:
q + sqrt(3)/1.
Therefore, the expression is equivalent to q + sqrt(3).
No latex
I apologize for the confusion in my previous response. Let's simplify the expression (q^4 - 3)/(q - 15) without using LaTex:
We start by factoring the numerator as a difference of squares.
q^4 - 3 can be written as (q^2)^2 - (sqrt(3))^2, which factors to (q^2 + sqrt(3))(q^2 - sqrt(3)).
Now, our expression becomes ((q^2 + sqrt(3))(q^2 - sqrt(3)))/(q - 15).
Next, we can simplify the expression by canceling out the (q^2 - sqrt(3)) terms in the numerator and denominator. This leaves us with:
(q^2 + sqrt(3))/(1), which simplifies to q^2 + sqrt(3).
Therefore, the expression (q^4 - 3)/(q - 15) is equivalent to q^2 + sqrt(3).