Can someone let me know if I hve the correct answer?
Divide and simplify
(x^2-16)/(49x+196)÷(x-4)/28
I came up with the answer 28/49
is this correct or can it be simplified more?
To divide and simplify the given expression, we can follow these steps:
Step 1: Rewrite the expression using the division sign as multiplication by the reciprocal:
[(x^2 - 16)/(49x + 196)] * [28/(x - 4)]
Step 2: Factor both the numerator and denominator of the first fraction to check for any common factors that can be canceled out:
[(x - 4)(x + 4)/(49x + 196)] * [28/(x - 4)]
Step 3: Simplify the common factors:
[(x + 4)/(49x + 196)] * [28/(x - 4)]
Step 4: Simplify further if possible. In this case, we notice that the denominator of the first fraction can be factored out as a common factor of 49:
[(x + 4)/(49(x + 4))] * [28/(x - 4)]
Step 5: Cancel out the common factor of (x + 4) from the numerator and denominator:
[1/49] * [28/(x - 4)]
Step 6: Multiply the numerators and denominators together:
28/(49 * (x - 4))
Step 7: Simplify the expression:
28/(49x - 196)
This is the simplified form of the given expression. Therefore, the correct answer is 28/(49x - 196).