What is the least common denominator of the equation 5x+5−1x2+2x−15=4x2+2x−15?(1 point)
Responses
(x+5)(x2+2x−15)(x2+2x−15)
left parenthesis x plus 5 right parenthesis left parenthesis x squared plus 2 x minus 15 right parenthesis left parenthesis x squared plus 2 x minus 15 right parenthesis
(x+5)(x2+2x−15)
left parenthesis x plus 5 right parenthesis left parenthesis x squared plus 2 x minus 15 right parenthesis
(x+5)(x−3)
left parenthesis x plus 5 right parenthesis left parenthesis x minus 3 right parenthesis
(x+5)
The least common denominator of the equation 5x+5−1x2+2x−15=4x2+2x−15 is (x+5).
To find the least common denominator of the equation 5x+5−1x^2+2x−15=4x^2+2x−15, we need to factor the denominators and find their common factors.
The factors of the quadratic denominators, x^2+2x-15 and 4x^2+2x-15, are (x+5)(x-3) and (x+5)(4x-3), respectively.
To find the least common denominator, we need to find the common factors of these two expressions. The only common factor is (x+5)(x-3).
Therefore, the least common denominator is (x+5)(x-3).
To find the least common denominator of the equation 5x + 5 − 1x^2 + 2x − 15 = 4x^2 + 2x − 15, we need to factor all the denominators of the equation and then find the least common multiple of those factors.
Let's start by factoring the denominators:
- The first denominator is 1, which does not need factoring.
- The second denominator is x^2 + 2x − 15. This can be factored as (x + 5)(x − 3).
- The third denominator is 4x^2 + 2x − 15. This cannot be factored further.
Now, we need to find the least common multiple of the factors. In this case, the least common multiple is (x + 5)(x − 3).
Therefore, the least common denominator of the equation 5x + 5 − 1x^2 + 2x − 15 = 4x^2 + 2x − 15 is (x + 5)(x − 3).